For the grits: Bring the half-and-half and 2 cups water to a boil in a large saucepan. Add 1 1/2 teaspoons salt and 1/2 teaspoon pepper. Add the grits while stirring constantly. Reduce the heat to a simmer and cook for 10 minutes. Add the Cheddar, Parmesan and butter, stirring constantly. Cook for 10 to 15 minutes more.
For the basil vinaigrette: Combine the basil, vinegar, honey, garlic, mustard and onions in a mixing bowl. Using an immersion blender, blend together into a paste. Drizzle in the vegetable oil, blending until well incorporated. Season with salt and pepper.
For the swordfish: Coat the fish with 2 tablespoons basil vinaigrette and season with salt and pepper. Grill for 2 minutes per side.
Spoon the grits in the center of a serving dish. Top with the fish and drizzle with some of the remaining vinaigrette.
This recipe was provided by a professional chef or restaurant and may have been scaled down from a bulk recipe. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.