Heat 1/4 cup extra virgin olive oil and the red pepper flakes in a large skillet over medium-low heat and gently cook for 3 minutes to infuse the oil.
Remove the pan from the heat and stir in the crushed or minced garlic for about 20 seconds, then add the canned crushed tomatoes.
Stir in 1 teaspoon sugar and 1/2 teaspoon salt, return to low heat, and simmer the sauce gently for 20 minutes, stirring occasionally.
While the sauce simmers, prepare the chicken: pat 2 chicken breasts dry and slice each breast horizontally to create thinner fillets.
Cover the fillets with plastic wrap or parchment and gently pound the thicker ends with a meat mallet or the base of a skillet so each fillet is an even thickness.
Season the chicken fillets with 1 teaspoon salt and 1/2 teaspoon black pepper.
Heat 2 tablespoons olive oil in a heavy skillet over medium-high heat until shimmering, then add the chicken fillets and cook 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 package directions; reserve 1 cup pasta cooking water, then drain.
Add the drained pasta to the simmering sauce with 1/4 cup of the reserved pasta water, toss the rigatoni in the sauce over low heat for 1 minute, adding more pasta water if the sauce is too thick.
Add 1 cup packed baby spinach and toss until wilted and evenly distributed through the pasta.
Season the pasta to taste with salt and pepper, top with the cooked chicken, and serve garnished with fresh parsley, grated parmesan, and a drizzle of extra virgin olive oil.
