Preheat the oven to 375°F. Spray a 9x13-inch baking dish with vegetable oil and set aside.
In a large saucepan, bring 10 cups of water to a boil. Stir in the grits and reduce the heat to medium-low. Cook, stirring constantly, until tender, 4 to 5 minutes. Stir in the cream, Gruyere cheese, Cheddar, garlic powder, and garlic salt and cook, stirring, until the cheese is melted and the mixture is well combined, about 5 minutes.
Pour into the prepared baking dish.
Bake until the top is set and golden, about 30 minutes; a few cracks might appear. Served warm, the grits will be soft and spoonable. They will firm up as they sit at room temperature. Sprinkle with paprika and chives just before serving. (See Cook’s Note.)
Store leftovers in a covered container in the refrigerator for up to 2 days. To reheat, slice the grits into squares and bake in a 350°F oven until warmed through.