Preheat oven to 375 degrees F (190 degrees C). Spray a mini muffin tin lightly with cooking spray.
Unroll crescent roll dough onto a lightly floured work surface and press into a 8x12-inch rectangle. Cut dough into 24 two-inch squares. Place each square into a muffin cup, gently pressing dough into the bottom and sides.
Heat olive oil in a 3-quart saucepan over medium heat. Add spinach and garlic; cook and stir until wilted, about 1 minute. Add artichokes, cream cheese, 3/4 of the mozzarella cheese, and Parmesan cheese. Cook and stir until cheeses are melted, about 2 minutes. Stir in pesto, salt, and pepper.
Push 1 teaspoon of the spinach mixture into each dough square; spread the remaining mozzarella cheese on top.
Bake in the preheated oven until golden brown, 15 to 17 minutes. Let cool in pan for 5 to 10 minutes before moving mini bites from the tray.