To make the dough, in an electric stand mixer fitted with the dough hook attachment add the warm milk + yeast and let sit for 10 minutes. Break up any yeast clumps. Add in 4 1/4 cups (531 g) flour, melted butter and sugar and run the machine on low for 1 minute. Add in the egg, salt and peppermint extract and run the machine on low for 2 minutes or until combined. The dough may stick to the bottom of the mixer, but if it's sticking to the sides, add the remaining flour in 1 tablespoon increments to keep the dough from sticking. Turn the mixer to medium and for 8-10 minutes more or until the dough is smooth, elastic and a ball has formed.
Lightly oil a large bowl, place the dough inside, turning to coat and cover with a clean, damp hand towel. Set in a warm, draft-free spot for 60 minutes or until double in size.
When the dough has doubled, mix the 1/2 cup (113 g) melted butter and peppermint extract in a small bowl. Set aside. Place 12 cupcake liners in the wells of a muffin tin.
To shape + fill the buns, place the dough on a floured-surface and roll to an 18x12 inch rectangle. Try to make the corners square. If the dough shrinks after rolling, let it rest 5 minutes and then continue rolling. Smear the peppermint-butter mixture over the top of the dough, leaving a 1/2-inch border along one long (18-inch) edge. Sprinkle the white and dark chocolate and the crushed candies over the top of the dough in a similar fashion. Starting at the 18-inch edge (with the filling all the way up to the edge), start rolling the dough onto itself and pinch the final edge to the dough log, to seal everything up. Roll the log so the seam side faces down. Using a sharp knife, cut 12 buns. Place each bun in one of the prepared muffin wells. Some of the center-cut buns may need a little nudging to fit, but do your best. It'll all work out. Promise. Cover loosely with plastic wrap or a damp towel and let rise for 35 minutes.
Heat oven to 350F (180 C). In a food processor fitted with the blade attachment pulse the crushed peppermint candies until fine. Add in the sugar and pulse until completely combined and the prettiest shade of pink. Set aside.
Once heated, bake the uncovered buns in the center of the oven for 25-30 minutes, or until golden and the internal temperature is 190F (88 C). Let cool 10-15 minutes. Brush the baked buns lightly with the melted butter and sprinkle with the peppermint candy sugar. Serve immediately! I like them slightly warm, always eating the center of the bun first and recommend a side of champagne to wash the whole thing down.
Thank you for baking these Holiday Chocolate Peppermint Breakfast Buns! Please tag @displacedhousewife @brianharthoffman @cloudykitchen #fomobaking if you make these beauties!