Heat oil in a large skillet over medium heat. Add shallots; cook, stirring, until soft, about 3 minutes. Add garlic; cook 1 minute more. Add spinach, tomatoes, salt, pepper flakes and pepper; cook, stirring, 2 minutes more. Remove from heat; let cool about 15 minutes.
Add ricotta; stir to combine. Season with salt and pepper. Pack about 1/2 cup spinach mixture on top of each fillet, matching the shape of the fillet. Place fillets on a rimmed baking sheet or in a glass baking dish; bake until cooked through, 15 minutes.