Cook the penne pasta in well-salted boiling water according to package directions.
Heat olive oil in a large skillet over medium heat and sauté chicken cubes until golden and cooked through (165°F); set chicken aside.
In the same pan, melt butter and cook onions and garlic until fragrant.
Whisk in flour to the butter mixture to create a roux, cooking for about 1 minute.
Slowly pour in the milk while whisking constantly to prevent lumps, heating until the sauce begins to thicken.
Stir in the Cajun seasoning, bell peppers, and jalapeños, cooking until the peppers are tender-crisp.
Add the parmesan cheese and stir until melted and smooth.
Return the cooked chicken to the skillet, fold in the cooked pasta, and toss to coat thoroughly before serving.