Cook gnocchi according to package instructions. Reserve a small amount of pasta water when straining.
Mix basil pesto and olive oil together and set aside for plating.
Heat skillet over medium heat, add butter to pan, cook over medium heat while stirring until it starts to brown but not burn. Add chopped garlic quickly and immediately add alfredo sauce and a little pasta water. Simmer for 2-3 minutes until sauce is smooth.
Add cooked gnocchi, grated parmesan, and a pinch of black pepper. Remove to serving plates, drizzle with pesto oil.