Heat the oven to 375°F and coat a 9-by-13-inch baking dish with cooking spray.
Scatter the dough pieces, ham and squeezed spinach evenly in the dish.
Whisk the eggs, milk, salt and black pepper in a large measuring cup and pour the mixture evenly over the dough.
Press any dry dough edges lightly into the custard and scatter the Swiss cheese over the top.
Bake uncovered for 35 to 42 minutes, until the center reaches 160°F, the egg is set and the exposed dough is deep gold.
Rest for 10 minutes before slicing so the soft layers hold together.