Preheat the oven to 350°F.
In a medium bowl, toss the scallops in the flour.
Heat 1 tablespoon of the oil in a large nonstick skillet over high heat. Add the scallops and brown on both sides, about 1-2 minutes per side. Remove from skillet and arrange in a casserole dish (a 7x11-inch size works well).
Heat 1 tablespoon of the oil in the same skillet over medium heat. Add the garlic and cook until golden, about 1 minute. Add the spinach and cook, stirring frequently, until the spinach wilts, about 4 minutes. Arrange the spinach over the scallops.
Heat 2 tablespoons of oil in the skillet over medium heat. Add the flour and cook, stirring constantly, until the flour turns golden, about 2 minutes. Add the milk, stirring constantly and bring to a simmer. Reduce the heat and continue to simmer and stir gently until the mixture thickens, about 2 minutes.
Stir in the Cheddar cheese and 2 tablespoons of the Parmesan cheese until melted. Stir in the sherry and pour the cheese mixture over the scallops and spinach in the casserole dish.
Top with the breadcrumbs and the remaining Parmesan cheese.
Bake for 12 to 15 minutes, or until browned and bubbly.