Cook the pasta according to package instructions in a large pot of salted boiling water until al dente. Drain and set aside, reserving 1/2 cup of pasta water.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.
Reduce the heat to low and stir in the heavy cream. Allow it to simmer for 2-3 minutes, stirring occasionally.
Add the basil pesto and Parmesan cheese to the skillet, stirring until the cheese is melted and the sauce is well combined. If the sauce is too thick, gradually add some reserved pasta water until you reach your desired consistency.
Toss the cooked pasta in the sauce until well coated. Season with salt and pepper to taste.
Serve immediately, garnished with fresh basil leaves if desired.