Preheat oven to 375 degrees F.
Drain artichokes and press with a paper towel to reduce some of the moisture. Roughly chop, pressing with a towel again, then place in a bowl. Add ricotta cheese.
Heat a large skillet over medium low heat and add 1 teaspoon olive oil. Add in shallots with a pinch of salt and cook until soft and translucent, about 5 minutes.
Add in garlic and spinach, tossing to coat and cooking until spinach is wilted. Transfer spinach mixture to the bowl with artichokes and ricotta, then add salt, pepper, ¼ cup parmesan and ½ cup mozzarella cheese. Stir to combine.
Drizzle pizza dough with 1 teaspoon olive oil and brush to coat. Sprinkle a bit of mozzarella cheese over top of the dough, then spread spinach ricotta mixture evenly over top. Cover with remaining parmesan and mozzarella cheeses.
Bake for 25-30 minutes, or until cheese is golden and bubbly.
