Bring a large pot of salted water to a boil and cook the pasta according to package directions until al dente.
While the pasta cooks, melt the butter in a large skillet over medium heat.
Add the minced garlic to the skillet and sauté for 1 minute until fragrant but not browned.
Whisk in the heavy cream and bring to a gentle simmer for 3 to 5 minutes until slightly thickened.
Stir in the capers, lemon zest, and lemon juice.
Drain the pasta, reserving a small amount of the cooking water.
Add the cooked pasta and grated Parmesan cheese to the skillet.
Toss the pasta until thoroughly coated, adding reserved pasta water if the sauce needs thinning.
Season with salt and pepper to taste.
Garnish with chopped parsley and serve immediately.