Cook the spaghetti 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, or until fragrant.
Reduce the heat to low and pour in the heavy cream. Stir to combine, then add the softened cream cheese, stirring until melted and smooth.
Gradually add the grated Parmesan cheese, stirring continuously until the cheese is fully melted and the sauce is creamy. If the sauce is too thick, add reserved pasta water a little at a time until desired consistency is reached.
Season the sauce with salt, black pepper, and red pepper flakes (if using). Stir to combine.
Add the cooked spaghetti to the skillet and toss to coat the pasta evenly with the sauce. Cook for an additional 2-3 minutes to heat through.
Remove from heat and garnish with chopped parsley before serving.