Position a rack in the lower third of the oven, place an inverted baking sheet on top and preheat to 500 degrees . In a large bowl, combine the olive oil, garlic and parsley; season with salt and pepper.
Using oiled hands, stretch the pizza dough to fit a parchment-paper-lined baking sheet. Spread 3 tablespoons of the garlic mixture on top, leaving a 1/2-inch border, then sprinkle with the mozzarella and 2 tablespoons parmesan. Toss the artichokes, tomatoes and spinach with the remaining garlic mixture and arrange on top of the cheese. Sprinkle the remaining 3 tablespoons parmesan on top. Place the baking sheet on the inverted baking sheet in the oven and bake until the crust is crisp and golden, 18 to 20 minutes.