Coat a 2–3-quart round baking dish with nonstick spray.
Arrange half the bread slices on the bottom of the dish. Top with half of each of the cream cheese, mozzarella, pesto, prosciutto, and tomatoes. Finish layering with the remaining ingredients.
Whisk eggs, milk, salt, and pepper. Pour the mixture over the layers; cover and chill for at least 2 hours, or as long as overnight. Remove from the refrigerator 20–30 minutes before baking. Bake the strata at 350° until puffed, golden brown, and lightly set in the center, about 1 hour. Allow the strata to rest for 10 minutes before unmolding.