Prepare the filling: In a small bowl, combine the brown sugar, granulated sugar, cocoa powder, cinnamon, and salt. Set aside. Melt butter and set aside.
If mixing by hand: Stir the ingredients together in the order above with a wooden spoon for several minutes, until the dough forms a wet, shaggy mass. Turn dough onto a floured surface and knead for 5 minutes. The dough will be very sticky and cling to the counter, but use as little flour as possible to prevent the dough from becoming tough. Once kneaded, scrape the dough into a lightly oiled bowl, turn once to coat, cover with plastic wrap, and let rise.
Begin the night before. If mixing by machine: In the bowl of a stand mixer, whisk together the eggs, egg yolks, sugar, butter, food dye, and vanilla extract. Add 2 cups flour, cocoa powder, yeast, and salt. Place buttermilk in a microwave safe measuring cup and microwave for 30 to 45 seconds, until it reaches the temperature required for the yeast. (Refer to the package directions for the specific temperature—Red Star Platinum is 120 to 130 degrees F). If the buttermilk curdles when heated, simply whisk it back together. Pour the heated buttermilk into the mixing bowl and stir by hand or with the mixer's paddle attachment until the ingredients are evenly moistened. Switch to the dough hook, then add the remaining 1 3/4 cups flour. Knead dough on low speed for 6 minutes. The dough should be soft, moist, and tacky, but not excessively sticky. If dough is too wet, add more flour 1 tablespoon at a time, until the correct texture is reached. Lightly spray a large, clean bowl with cooking spray, then transfer dough to the bowl, turning once to coat. Cover bowl with plastic wrap and let rise in a warm, draft-free place until doubled in size, 2 to 2 1/2 hours.