Bring a large pot of salted water to a rolling boil for the rigatoni. Add the rigatoni and cook until al dente according to package directions. Reserve 1 to 2 tablespoons of the pasta cooking water, then drain the rigatoni and set aside.

Pat the chicken dry and cut into roughly 1-inch cubes. Season the chicken evenly with salt, freshly ground black pepper, and smoked paprika, then toss with the all-purpose flour to coat lightly.

In a large skillet over medium-high heat, cook the bacon until crisp. Transfer to a paper towel-lined plate to drain and crumble when cool. Reserve about 1 tablespoon of the bacon fat in the pan.

Add olive oil to the skillet with the reserved bacon fat and heat until shimmering. Add the floured chicken in a single layer and sear until golden and cooked through, about 3 to 4 minutes per side. Remove the cooked chicken to a plate and keep warm.

Reduce heat to medium and add the unsalted butter. When melted and foaming, add the minced garlic and cook until fragrant and lightly golden, about 45 to 60 seconds.

Stir in the tomato paste and cook briefly, then pour in the chicken broth while scraping up any browned bits from the bottom of the pan. Bring to a gentle simmer.

Whisk the heavy cream into the skillet and simmer for 2 to 3 minutes until the sauce begins to thicken slightly.

Lower the heat and stir in the freshly grated Parmesan until melted and the sauce turns glossy. Season with salt and freshly ground black pepper to taste. If the sauce is too thick, thin with a tablespoon or two of the reserved pasta water.

Return the seared chicken to the skillet, add the drained rigatoni, and toss gently to coat everything evenly with the sauce. Warm through for 1 to 2 minutes.

Stir in the lemon juice and crushed red pepper flakes if using, then fold in the crumbled bacon and chopped parsley. Adjust seasoning as needed and serve immediately with extra grated Parmesan and parsley for garnish.