Step 1

Heat butter in a medium saucepan over low heat until melted and just beginning to foam. Whisk in 2 Tbsp. flour; cook, stirring often, until flour begins to smell nutty, about 5 minutes. Whisk in milk; cook gently over low heat, stirring often, until mixture thickens, about 20 minutes. Add cheese; whisk until combined. Season Mornay sauce to taste with cayenne, nutmeg, and salt. DO AHEAD Mornay sauce can be made 2 days ahead. Cover and chill.

Step 2

Cook bacon in a medium skillet over medium heat until crisp and browned; transfer to paper towels to drain; set aside.

Step 3

Build a medium-hot fire in a charcoal grill, or heat a gas grill to high. Place onion in a medium bowl. Drizzle with 2 tsp. oil; season with salt and pepper. Grill onion, turning occasionally, until tender, about 10 minutes. Transfer to a large bowl. Place apples in same medium bowl; drizzle with 2 tsp. oil. Grill, turning occasionally, until charred in spots and tender, about 12 minutes.

Step 4

Transfer apples to large bowl with onion; add rosemary, sage, thyme, and reserved bacon. Toss to combine. Season with salt and pepper and cover; keep warm.

Step 5

Rewarm Mornay sauce over medium-low heat, stirring occasionally. Stir in crème fraîche and set aside.

Step 6

Divide pizza dough into 2 equal pieces; shape each piece into a ball. Roll out each ball on a floured surface to an 8-inch round. Brush with 1 tsp. oil; place on grill, oiled sides down. Brush other sides with remaining 1 tsp. oil.

Step 7

Grill flatbreads, watching carefully and moving as needed to promote even cooking and prevent burning, until charred and crisp on bottom, 1–2 minutes. Turn flatbreads over and cook until crisp and cooked through, 1–2 minutes longer. Transfer flatbreads to a work surface.

Step 8

Spread half of warmed Mornay sauce over each flatbread. Top sauce with apple mixture. Cut flatbreads into wedges.