In a large skillet over medium-high heat, add the oil and melt the butter. Add the garlic and cook, stirring occasionally, until fragrant, about 1 minute. Add the wine, salt, red pepper flakes, and black pepper, to taste, and bring to a simmer. Let the liquid reduce by half, about 2 minutes.
Add the shrimp and artichokes and cook, stirring occasionally, until the shrimp are just pink, 2 to 4 minutes. Stir in the basil. Season with salt and serve over pasta, rice, or with crusty bread. Sprinkle with the cheese.