Preheat your oven to 375°F (190°C).
In a large skillet, heat the extra virgin olive oil over medium heat. Add the chopped yellow onion and carrots, cooking until the onion is translucent, about 5 minutes.
Add the cubed chicken breasts to the skillet. Season with garlic powder, kosher salt, and black pepper. Cook until the chicken is browned and cooked through, around 7-10 minutes.
Stir in the butter, fresh thyme leaves, paprika, and cayenne pepper. Allow everything to melt and combine for about 2 minutes.
Pour in the low sodium chicken broth and milk. Bring the mixture to a gentle simmer, stirring occasionally.
Meanwhile, cook the short cut pasta in a separate pot according to package instructions until al dente. Drain and set aside.
Add the cooked pasta and broccoli florets to the skillet. Stir to combine everything, ensuring that the pasta and broccoli are well coated in the creamy sauce.
Transfer the entire mixture into a greased baking dish. Sprinkle the grated Parmesan cheese and shredded cheddar cheese over the top.
Bake in the preheated oven for about 25-30 minutes or until the cheese is bubbly and golden brown.
Once out of the oven, let the casserole cool for a few minutes before serving.