In a pot of salted, boiling water, add the pasta and cook to al dente, according to the package directions.
Drain the pasta and set it aside.
Preheat the oven to 400 degrees F.
In a medium bowl, add the cherry tomatoes, 2 tablespoons of the olive oil, the extra salt, and the extra black pepper and toss to combine.
On a rimmed baking sheet, add the tomatoes and spread them out in a single layer.
Roast the tomatoes until they are blistered, about 20 minutes. Set the tomatoes aside.
Season the chicken breasts with 1/4 teaspoon of the remaining salt, 1/4 teaspoon of the remaining black pepper, the garlic powder, and the paprika.
In a large skillet over medium heat, add 2 tablespoons of the remaining olive oil.
Add the chicken breasts to the hot oil and cook, flipping them once, until they are browned on the edges and they reach an internal temperature of 165 degrees F, about 5-8 minutes per side.
Transfer the chicken breasts to a clean plate.
Add the onions to the same skillet and cook, while adding the extra olive oil as needed and stirring occasionally, until they are slightly caramelized, about 10 minutes.
Add the garlic to the onion mixture and cook, while stirring, until fragrant, about 30 seconds.
Add the pesto to the onion mixture and stir to combine.
Add the heavy cream to the onion mixture and stir gently to combine.
Bring the cream mixture to a simmer.
Add the cooked pasta and the roasted tomatoes to the skillet and cook, while stirring, until heated through, about 2-3 minutes.
Slice the chicken breasts, then add the slices to the pasta mixture.
Top the pasta mixture with the parmesan cheese and the red pepper flakes.
Serve.