Creamy Cajun Chicken Pasta

1 lb boneless skinless chicken breasts (shrimp can be substituted)
2 Tbsp olive oil, divided
6 tsp cajun seasoning, divided (recipe in notes below)
12 oz dry linguine or fettuccine pasta
2 Tbsp butter
1 clove garlic, minced
3 Tbsp flour
1 1/2 cups milk
1/2 cup heavy cream or half and half
1/3 cup shredded parmesan cheese
1 medium red bell pepper, sliced into thin strips then strips halved (about 1 1/2 cups)
1 medium yellow bell pepper, sliced into thin strips then strips halved (about 1 1/2 cups)
1/2 large red onion, sliced into thin strips
2 cups sliced button mushrooms (about 8)
Fresh parsley, for garnish