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Drizzle chicken with one tablespoon olive oil and toss to coat. Sprinkle over the Italian seasonings and 1 tsp salt and freshly ground pepper as you toss the chicken to ensure it’s evenly coated on all sides.
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Bring water to a boil in a large pot for the pasta while cooking the chicken and sauce.
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In an oven-safe skillet over medium heat, add 2 tablespoons of olive oil or enough to coat the bottom of the pan. Cook chicken about 4-5 minutes, flip once, reduce heat to low, and continue to cook about 3-4 minutes or until cooked through. Set aside.
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In the same pan, reduce heat to medium-low and add 2 tablespoons butter to melt. Add in the onion and sauté until translucent, about 2-3 minutes. Add in garlic and sauté until fragrant.
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Pour in the milk and sprinkle in Cajun seasonings and red pepper flakes (if using) and salt and pepper to taste (about ½ tsp each). Add in sun-dried tomatoes and broccoli and bring to a low simmering boil until the broccoli softens, about 5 minutes.
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Meanwhile, cook the rigatoni to al dente.
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Into the sauce, add in the spinach leaves, stirring into the sauce until they wilt. Fold the cooked rigatoni, chicken, and pesto into the sauce until it’s evenly incorporated.