Heat 1/4 cup extra virgin olive oil and 2 teaspoons red pepper flakes in a large skillet over medium-low heat and cook gently for about 3 minutes to infuse the oil.
Remove the pan from the heat, add the 6 crushed or minced garlic cloves, and stir for about 20 seconds until fragrant.
Stir in the 28 oz can of crushed Italian tomatoes, 1 teaspoon sugar, and 1/2 teaspoon salt, then simmer on low for 20 minutes, stirring occasionally.
While the sauce simmers, prepare the chicken: pat 2 chicken breasts dry and slice each breast horizontally to make thinner fillets.
Cover the fillets with plastic wrap or parchment and gently pound with the base of a heavy skillet or meat mallet until even in thickness.
Season the chicken on both sides with 1 teaspoon salt and 1/2 teaspoon black pepper.
Heat 2 tablespoons olive oil in a heavy skillet over medium-high until shimmering, then sear the chicken fillets 3–4 minutes per side until golden and cooked through; transfer to a plate and tent with foil.
Bring a large pot of water to a boil, add 1 tablespoon salt, and cook 10 oz rigatoni for 1 minute less than the package directions. Reserve 1 cup of the pasta cooking water, then drain.
Add the drained pasta to the tomato sauce with 1/4 cup of the reserved pasta water and toss over low heat until the pasta is evenly coated, adding more pasta water if needed to loosen the sauce.
Toss in 1 cup packed baby spinach and stir until wilted and combined with the pasta.
Adjust seasoning with salt and pepper to taste, slice or place the chicken on top, and serve garnished with fresh parsley, grated parmesan, and a drizzle of extra virgin olive oil.