Preheat charcoal or gas grill with two grilling zones: direct grilling over high heat (400°) and indirect grilling over medium-high heat (375°). Spray a 15x10-inch rimmed baking pan with nonstick spray; set aside.

Roll out one pastry crust on lightly floured surface. Cut pastry into 17½x12½-inch rectangle. Fold pastry in half and place in prepared pan. Unfold and gently ease into bottom and sides of prepared pan. Whisk together egg yolk and water; lightly brush with some egg mixture on edges of pastry crust.

Toss chicken with ¼ cup barbecue sauce. Layer chicken mixture, carrot, red onion slices, mozzarella, and blue cheese on top of crust. Drizzle with remaining ½ cup barbecue sauce.

Roll remaining pastry crust into 15½x10½-inch rectangle. Cut pastry into 1-inch wide strips. Weave strips in lattice pattern over filling in baking pan; press ends to edges of bottom crust. Trim excess dough from strips, if necessary. Brush lattice with remaining egg yolk mixture; sprinkle with sea salt.

Place pie over indirect heat. Close grill lid; grill 30 to 35 minutes or until filling begins to bubble and top is golden brown, rotating pan halfway through. Move slab pie to direct heat. Grill 10 to 12 minutes or until crust is golden brown. Remove from heat; cool 10 minutes on wire rack before serving.