Instruction

1. Beat bread flour, whole-wheat flour, milk, and eggs with a stand mixer fitted with the dough hook attachment on low speed until a shaggy dough forms, about 1 minute. Cover bowl tightly with plastic wrap, and refrigerate 30 minutes.
2. Return chilled dough in bowl to stand mixer fitted with dough hook. Add sugar, salt, and yeast to dough, and beat on low speed until just combined, about 2 minutes. Add butter, and beat until just incorporated, about 1 minute. Increase mixer speed to medium-high, and beat until dough pulls away from sides of bowl and is glossy and elastic, 8 to 10 minutes. (Dough will be very sticky.) Transfer dough to a lightly greased (with cooking spray) large bowl, and cover tightly with plastic wrap. Let rest at room temperature until slightly risen, 1 hour to 1 hour and 30 minutes. Transfer to refrigerator, and chill at least 8 hours or up to 16 hours.
3. Cook bacon in a medium-size nonstick skillet over medium-low, stirring occasionally, until fat is completely rendered and bacon is crispy, 8 to 10 minutes. Using a slotted spoon, transfer bacon to a plate lined with paper towels; reserve drippings in skillet. Add onion, salt, pepper, and garlic to skillet; cook over medium-low, stirring often, until onion and garlic are tender but have not developed any color, 1 to 2 minutes. Reduce heat to low; stir in tomato and brown sugar; cook, stirring occasionally, until tomato breaks down and mixture thickens and becomes jammy in consistency, 20 to 25 minutes. Remove skillet from heat, and stir in vinegar and reserved bacon until mixture is well combined. Transfer jam to a medium bowl; cover with plastic wrap, and refrigerate until ready to use.
4. Line 2 rimmed baking sheets with parchment paper. Turn brioche dough base out onto a lightly floured work surface, and roll into a 13- x 20-inch rectangle (about 1/4 inch thick). Spread pesto evenly over dough, leaving a 1/2-inch border along one short edge; sprinkle evenly with cheese. Roll dough up toward 1/2-inch border to create a log (being careful not to roll too tightly); cut crosswise into about 12 (1 1/2-inch-thick) rounds, tucking ends of dough underneath each round. Arrange rounds evenly on prepared baking sheets, leaving at least 2 to 3 inches between rounds. Cover loosely with lightly greased (with cooking spray) plastic wrap, and let stand at room temperature until dough is doubled in volume and soft to the touch, about 2 hours. Preheat oven to 325°F with racks in top third and bottom third positions during final 20 minutes of dough proofing time.
5. Uncover proofed scrolls, and gently brush with lightly beaten egg. Bake in preheated oven until scrolls are golden brown, 20 to 25 minutes, rotating baking sheets from front to back and between top and bottom racks halfway through baking time. Immediately top each scroll with about 1 1/2 tablespoons reserved bacon jam. Garnish with basil and additional Asiago cheese, if desired. Transfer scrolls to a wire rack, and let cool slightly, about 10 minutes. Serve warm.