Cook the pasta in salted boiling water until al dente.
Drain and set aside.
Set up three shallow bowls: one with flour, one with beaten egg, and one with breadcrumbs mixed with Cajun seasoning.
Dredge each chicken breast in flour, dip in egg, then coat with breadcrumb mixture.
Heat vegetable oil in a skillet over medium-high heat.
Cook the chicken until golden brown on both sides and cooked through.
Remove and let it rest.
In the same pan, add olive oil and sauté the vegetables until tender.
Add the mushrooms and peppers.
Add heavy cream and Parmesan cheese to the vegetables.
Simmer until the sauce thickens.
Toss pasta with the sauce and serve sliced chicken on top.