Heat the oven to 400°F and lightly grease a 12-inch pizza pan or baking sheet. Unroll the refrigerated pizza dough onto the pan, pressing it into a 12-inch round with a slightly raised edge, then prick the center lightly with a fork.

Partially bake the crust for 5–6 minutes, just until it begins to set. This short first bake helps keep the French-toast mixture and apple juices from making the center soggy.

Whisk the eggs, milk, maple syrup or sugar, vanilla, cinnamon, nutmeg, and salt in a small bowl. Remove the crust from the oven and brush or spoon the mixture over the surface, keeping most of it in the center instead of allowing it to pool around the edge.

Toss the sliced apples with the brown sugar, flour, and cinnamon. Arrange the apples over the crust, cut the cold butter into small pieces, and scatter it over the apples along with the optional chopped pecans or walnuts.

Bake for 15–19 minutes, until the apples are tender, the crust is golden, and the egg mixture is set. Stir the confectioners’ sugar, milk, and vanilla into a thin glaze, then drizzle it over the warm pizza.

Let the breakfast pizza rest for 5 minutes before slicing into 8 wedges. Serve warm while the glaze is glossy and the cinnamon apple topping is fragrant.