Heat 1 tablespoon oil in a large nonstick pan over medium-high heat. Add shallot and cook, stirring often, until softened, about 1 minute. Add spinach in batches and cook, stirring, until wilted, 3 to 5 minutes. Stir in dill, parsley, garlic and pepper. Cook, stirring, for 1 minute. Transfer the spinach mixture to a large mixing bowl. Stir in ricotta and feta.
Rub bell peppers with the remaining 1 tablespoon oil and sprinkle with salt. Divide the spinach mixture among the peppers and top each with 1 tablespoon mozzarella. Place in an 8-inch-square baking dish.
Bake until the peppers are tender, 30 to 35 minutes. Let cool for 5 minutes before serving.