This challenging recipe requires three days to make and precise measurements, but it's worth the effort.
Make the levain: In a 4-cup glass measuring cup, combine apple and water. Use an immersion blender or food processor to puree. In the bowl of an electric mixer fitted with the dough hook, combine the apple mixture with 300 grams (10 1/2 ounces) high-gluten flour. Beat on medium-low until a stiff dough forms, about 3 minutes.
Place levain into a large clean container. Cover tightly, and let rise in a very warm place for at least 24 and up to 48 hours. (The temperature should be 79 degrees. A good place would be near, but not on, a stove or heating source -- do not rise in an oven.) The dough should rise until tripled in bulk and then it will, most likely, fall.
Remove 150 grams (5.4 ounces) of levain from the center of the risen dough, and discard the remaining levain. In the bowl of an electric mixer fitted with the dough hook, combine levain with 150 grams (5.4 ounces) high-gluten flour and 1/3 cup warm water until a uniform dough is formed. Transfer to a work surface, and knead briefly. Shape into a ball, return to the mixer bowl, and cover with plastic wrap. Set aside in a warm place until tripled in size, about 4 hours. Repeat this process twice. The levain is now ready to use. Be sure to always take the levain from the center of the levain because the natural yeasts are more concentrated there.
Make the sponge: In a glass measuring cup, combine sugar and scant 1 cup water. Stir to dissolve sugar. In the bowl of an electric mixer fitted with the dough hook, combine high-gluten flour, sugar mixture, and prepared natural levain. Starting on low speed, beat until flour is incorporated. Increase speed to medium, and beat until dough is smooth, about 6 minutes start to finish.
Add cold butter a bit at a time, while beating on low speed for about 1 minute. Increase speed to medium, and beat until smooth, 6 to 8 minutes more. Scrape down bowl as necessary. If necessary, switch to paddle attachment briefly to help incorporate butter. Add egg yolks, and beat on low until incorporated. Increase speed to medium, and continue beating until dough is shiny, elastic, and comes away from sides of bowl. (It will make a slapping sound when the speed is increased) Cover tightly with plastic wrap, and let stand in a very warm place for 12 hours. (The temperature should be 79 degrees. A good place would be near, but not on, a stove or heating source -- do not rise in an oven.) The dough should triple in bulk.
Make the dough: In the bowl of an electric mixer fitted with the paddle attachment, cream together the butter and honey until smooth, about 1 minute. Set aside. In a liquid measuring cup, combine 80 ml (scant 1/2 cup) water, the sugar, salt, vanilla extract, and lemon and orange oils. Stir to combine. Sprinkle the high-gluten flour over the risen sponge. Beat on low until all the flour is incorporated, about 3 minutes.
With machine running on medium-low speed, gradually add the liquid mixture; if the dough begins to separate, stop adding the liquid and briefly increase speed to medium high until dough just comes back together. Reduce speed, and continue adding liquid. It should take about 4 minutes to add all of the liquid. Increase speed to medium high, and beat until dough is smooth, shiny, and elastic, about 5 minutes more.
With machine running on medium speed, add the creamed honey mixture all at once. Beat until incorporated, about 4 minutes, scraping down the sides of the bowl as necessary. Add egg yolks, and beat on medium low until incorporated and dough is shiny and elastic, about 4 minutes. Add raisins and orange peel, and beat until just incorporated, about 2 minutes more.
Lightly oil work surface. Turn dough out onto surface, and cut into six 190-gram (6.8-ounce) pieces and four 250-gram (9-ounce) pieces. Work each piece of dough into a ball. Place smaller pieces into 3 1/2-inch-baking papers and large pieces in 4 1/2-inch-baking papers. Place filled papers onto baking sheets. Place each baking sheet into a large plastic bag, and seal. Set aside in a very warm place until tripled in volume, 6 to 8 hours. (The temperature should be 79 degrees. A good place would be near, but not on, a stove or heating source -- do not rise in an oven.)
Heat oven to 375 degrees. Make the topping: In the bowl of a food processor, combine almonds, flour, and confectioners' sugar. Process until fine. Transfer to a medium bowl, and add grapeseed oil and egg whites. Stir to combine. The glaze should be thick and almost pastelike.
Gently spoon about 2 tablespoons glaze over the top of each risen brioche to cover. Sprinkle with whole almonds (about 6 per loaf). Sprinkle heavily with pearl sugar. Bake until golden brown and set, 25 to 30 minutes for the small, 30 to 35 minutes for the large.