First, stir together cajun seasoning ingredients in a small bowl: oregano, paprika, salt, thyme, garlic powder, onion powder, black pepper and red pepper.
In a large skillet over the stove top on medium-high heat, add 2 Tbsp. olive oil and chicken pieces. Sprinkle 1/2 of the cajun seasoning mixture over the chicken pieces and stir, while cooking, just until the chicken is no longer pink and cooked through.
Remove the cooked chicken to a plate using a slotted spoon. Leave the liquids in the skillet.
Add one more Tablespoon of olive oil to the skillet, then add diced red and yellow pepper, diced mushrooms, and minced garlic. Stir and saute over the stovetop on medium heat, until the peppers and mushrooms are tender and have reduced.
Pour the chicken broth into the skillet with the peppers and mushrooms, then add the last half of the cajun seasoning and stir.
Next, add the linguine, breaking the pasta in half before putting it in.
Push the pasta completely under the liquid, cover the skillet, and bring it to a boil. After it has come to a boil, turn down the heat slightly so it's still at a high simmer and then allow it to cook, covered, until the pasta is tender. Stir occasionally, then replace the lid.
When the pasta is tender and liquids have mostly absorbed, stir in the cooked chicken chunks, softened cream cheese, and shredded parmesan and toss until the cheeses melt completely. Serve immediately.