Combine the diced tomatoes, chopped basil, minced garlic, olive oil, balsamic vinegar, salt, and black pepper in a small bowl. Stir gently and set aside.

Bring a large pot of generously salted water to a boil. Cook the penne according to the package directions until al dente. Reserve about ½ cup of pasta water, then drain the pasta.

Cut the chicken into bite-size pieces. Toss with olive oil, Italian seasoning, paprika, salt, black pepper, and red pepper flakes if using.

Heat a large skillet over medium-high heat. Add the seasoned chicken in a single layer and cook until browned and completely cooked through. The chicken should reach an internal temperature of 165°F (74°C). Transfer to a clean plate.

Reduce the skillet heat to medium-low. Add the heavy cream and bring it to a gentle simmer. Gradually add the Asiago, white cheddar, and Parmesan, stirring continuously until melted and smooth.

Add the chicken broth and continue cooking gently until the sauce thickens and coats the back of a spoon.

Add the cooked penne to the cheese sauce and toss until evenly coated. If the sauce is too thick, add reserved pasta water a little at a time.

Return the cooked chicken to the skillet and gently fold it into the creamy pasta. Taste and adjust the seasoning if needed.

Add the Tomato Topping

Spoon the fresh tomato and basil mixture over the pasta just before serving. Serve immediately with extra Parmesan or fresh basil if desired.