This classic French flatbread from the region of Provence is shaped into an oval then scored so it looks an ear of wheat when baked.
In a large bowl, sprinkle yeast and sugar over warm water; let stand until creamy, about 5 minutes. In another bowl, whisk together both flours and kosher salt. Add flour mixture and oil to yeast mixture, stirring until a wet, ragged dough forms. Transfer to a floured work surface; knead with floured hands until dough is smooth, elastic, and tacky but no longer sticky, about 5 minutes. Transfer to a bowl lightly brushed with oil; loosely cover with a towel. Let stand in a warm place until doubled in volume, 1 1/2 to 2 hours, or refrigerate up to 2 days.
Preheat a wood-burning or regular oven to 500 degrees. (If using a regular oven, set rack in lowest position and line with a pizza stone or metal baking sheet.) Punch down dough; divide in half. Transfer each half to a sheet of parchment (at least 15 inches long) lightly dusted with flour. Roll out each to an approximately 13-by-7-inch oval. With a baker's blade or the tip of a knife, and starting 1 1/2 inches below top of each oval, make a 10-inch vertical slash in each dough until you reach 1 1/2 inches from bottom. Make 1 1/2-inch-long diagonal slashes, about 1 inch apart, on each side of vertical slashes. Make 1/2-inch-long diagonal slashes along edges, if desired. Pull edges of each dough outward slightly to open slashes. Loosely cover; let stand in a warm place until doubled in volume, 30 to 40 minutes. Whisk together egg yolks and milk. Brush doughs with egg wash; sprinkle evenly with rosemary, sesame and nigella seeds, and flaky salt.
Transfer 1 dough on parchment to oven (on pizza stone, if using). Bake until puffed and golden brown, 8 to 10 minutes. Repeat with second dough. Fougasse is best served the same day, but can be stored in an airtight container at room temperature up to 1 day.