Bring a large pot of salted water to a boil. Add the spaghetti and cook according to package instructions until al dente, about 8-10 minutes. Drain and set aside.
In a large skillet over medium heat, melt the butter with the olive oil.
Add the minced garlic to the skillet and sauté for 1-2 minutes until fragrant but not browned.
Stir in the lemon juice and lemon zest, then add the heavy cream. Cook for 2-3 minutes, stirring occasionally, until the sauce slightly thickens.
Add the cooked spaghetti to the skillet and toss to coat evenly with the lemon sauce.
Remove from heat and stir in the grated Parmesan cheese, salt, and black pepper until the cheese melts and the sauce is creamy.
Allow the pasta to cool completely before transferring it to an airtight container for storage.
Refrigerate the pasta for up to 3 days. To serve, reheat gently in a skillet over low heat, adding a splash of water or cream if needed to loosen the sauce.
Garnish with chopped fresh parsley before serving.