Cook penne pasta in salted boiling water until just al dente. Drain and set aside while you prepare the sauce.
Heat olive oil in a large skillet over medium heat. Add chicken and cook until golden on the outside and fully cooked inside.
Remove chicken and set aside. In the same pan, melt butter and sauté onion and garlic until soft and fragrant.
Add flour and stir continuously until it forms a thick paste. Cook for 1–2 minutes until it smells slightly nutty.
Slowly pour in milk while stirring. Keep heat medium-low and mix until the sauce becomes smooth and creamy.
Stir in Cajun seasoning, bell peppers, and jalapeños. Simmer until peppers are slightly tender but still crisp.
Add parmesan cheese and stir until melted and thickened into a silky sauce.
Return cooked chicken to the pan and mix well until fully coated in sauce.
Add pasta and toss everything together until evenly combined and creamy.