Make the Cajun Seasoning: In a small bowl, whisk together the smoked paprika, garlic powder, onion powder, cayenne pepper, oregano, thyme, salt, and black pepper. Set aside.

Cook the Pasta: Bring a large pot of salted water to a boil. Add the pasta and cook according to package instructions until al dente. Reserve 1 cup of pasta water, then drain the pasta.

Season and Cook Chicken: While pasta cooks, toss the cubed chicken with half of the prepared Cajun seasoning. Heat olive oil in a large Dutch oven over medium-high heat. Add the chicken and cook until golden and cooked through, about 5-7 minutes. Remove chicken from the pot and set aside.

Start the Sauce: In the same pot, melt the butter over medium heat. Add the diced onion and cook until soft, about 3-4 minutes. Stir in the minced garlic and the remaining Cajun seasoning, cooking for 1 minute until fragrant.

Make the Roux and Thicken: Sprinkle the flour over the onions and cook, stirring constantly, for 1 minute. Slowly whisk in the milk until smooth, then whisk in the heavy cream. Bring to a simmer and cook until thickened, about 2-3 minutes.

Melt the Cheese: Reduce heat to low. Add the shredded cheddar, Monterey Jack, and Parmesan in handfuls, stirring until each addition is fully melted before adding the next. Stir until the sauce is completely smooth.

Combine and Serve: Add the cooked pasta and chicken to the cheese sauce. Stir to combine. If the sauce is too thick, add a splash of the reserved pasta water. Serve immediately.