Bring a large pot of salted water to a boil. Cook the pasta according to the package directions until al dente. Reserve 1 cup of the pasta water before draining.
Meanwhile, cook the bacon in a large skillet over medium heat until crisp. Transfer the bacon to a paper towel-lined plate, leaving about 2 tablespoons of bacon fat in the skillet.
Add the garlic to the skillet and cook for 30 seconds, stirring constantly, until fragrant.
Stir in the tomato paste and red pepper flakes. Cook for 1-2 minutes, stirring frequently, until the tomato paste darkens slightly.
Pour in the heavy cream and stir until smooth. Bring to a gentle simmer and cook for 3-4 minutes until the sauce begins to thicken.
Stir in the Parmesan cheese until melted, then return the bacon to the skillet.
Add the cooked pasta and toss until evenly coated in the sauce. If needed, add a splash of the reserved pasta water to loosen the sauce.
Taste and season with salt and black pepper as needed.
Garnish with fresh parsley, extra Parmesan cheese, and additional red pepper flakes before serving.