In a small pot, cover the wheatberries with 1/2 inch of water and add a pinch of salt. Bring to a boil, then simmer for 1 hour, or until the wheatberries are tender. Drain, dry, and set aside.
Heat together the milk and water to between 105 degrees and 110 degrees. Pour into a mixing bowl. Sprinkle the yeast on top, then add 1 tablespoon of the sugar and allow the yeast to "proof" (stand) for 10 minutes.
Using a dough-hook attachment, mix at low speed. Beat together 1 egg and oil and add to mixture. Beat in 2 cups bread flour, the whole-wheat flour, salt, and remaining sugar; mix at moderate speed until flour is incorporated and dough moves as a mass, about 4 minutes. Cover with plastic wrap; set aside to rise in a warm place until dough has doubled in bulk.
Heat oven to 375 degrees. Line a baking sheet with parchment paper. Add the wheatberries to the dough and mix them in by hand. Turn the dough (it will be quite sticky) onto a floured work surface; coat it lightly to make it manageable, but don't work in any extra flour. Divide the dough in half, then in half again. Roll these pieces into short tubes and cut into three equal parts. Roll each of these into a ball and place on baking sheet at least 3 inches apart. Beat remaining egg and brush onto buns. Sprinkle with sesame seeds. Set aside in a warm place to double in bulk.
Bake for 15 minutes, or until golden brown.