Preheat the oven to 375 degrees F. Spray a 2-quart casserole dish with cooking spray.
Heat the oil in a large non-stick skillet over medium-high heat. Add the shallot and garlic and cook, stirring, until soft, about 2 minutes. Add the red pepper flakes and cook, stirring, for 1 minute. Turn the heat off and stir in the artichokes, spinach, yogurt, cream cheese, 1 cup of the mozzarella and salt and pepper to taste; mix well together. Place the mixture in the prepared casserole dish and evenly top with the Parmesan and remaining 1/2 cup mozzarella. Bake until browned and bubbly, about 40 minutes.