Bring a large pot of salted water to a boil. Cook pasta according to package directions until al dente. Reserve 1 cup of pasta water, then drain the pasta and set aside.

While pasta cooks, toss chicken pieces with 2 tbsp of Cajun seasoning. Heat olive oil in a large skillet over medium-high heat. Add chicken and cook for 5-7 minutes until golden and cooked through. Remove chicken and set aside.

In the same skillet, melt butter over medium heat. Add minced garlic and cook for 30 seconds until fragrant. Whisk in flour and cook for 1 minute, stirring constantly.

Gradually whisk in chicken broth, then evaporated milk, until smooth. Bring to a simmer and cook for 2-3 minutes until thickened.

Reduce heat to low. Stir in cubed cream cheese until melted. Add shredded cheddar and Gruyère in handfuls, stirring until each batch is melted before adding the next. Season sauce with more Cajun seasoning to taste.

Add the cooked pasta and chicken to the cheese sauce. Stir to combine. If needed, thin the sauce with reserved pasta water. Serve immediately.