Prepare the scallops: Pat them completely dry with a paper towel. Season evenly with 1 teaspoon salt, smoked paprika, cumin, and several grinds of black pepper.
Cook the grits: Heat the milk in a medium saucepan over medium-high heat. When it just starts to form little bubbles, stir in the grits. Reduce heat to medium and cook, stirring frequently, until thick and creamy, about 4–5 minutes.
Prepare the basil: Pluck the leaves from the sprigs and finely chop them.
Mix in cheese and basil: Stir most of the chopped basil into the grits along with goat cheese, Parmesan, 1 tablespoon butter, 1 teaspoon salt, and several grinds of pepper. Turn off the heat and cover.
Sear the scallops: Heat a 12-inch stainless steel or cast iron skillet over medium-high heat. Test by flicking a drop of water onto the pan—if it skitters, it's ready. Add 2 tablespoons olive oil and swirl to coat. Once shimmering, place scallops in the pan, leaving space between them. Cook undisturbed for 2 to 3 minutes until the bottom is golden brown. Flip and add 2 tablespoons butter, tilting the pan to baste the scallops until the second side is golden brown, another 1 to 2 minutes.
Finish the grits: Stir the grits well and loosen with a splash of milk if needed for a risotto-like texture.
Serve: Spoon the grits onto plates or bowls, top with scallops, and drizzle with any leftover pan juices. Garnish with the remaining basil.