Bring water to a boil and cook your pasta according to the package directions. Once ready, reserve 1 cup of pasta water, drain, and set the pasta aside.
Cook the chicken:
On a flat surface, pat dry the chicken breasts. Slice them through the middle to butterfly them into 4 pieces. Distribute 1 ½ teaspoons of seasoning on both sides of the chicken breasts.
Heat a skillet over medium-high heat. Once hot, melt 1 tablespoon of butter. Place the chicken breasts on the pan and cook for 3 to 4 minutes. Flip the chicken breasts over, and cook for another 4 minutes on the other side. Remove the chicken from the pan onto a plate and leave any tidbits on the pan for extra flavor.
Make the sauce:
Add the remaining 2 tablespoons of butter to the pan and melt it while scraping the tidbits with a spatula. Add the remaining ½ teaspoon Cajun seasoning onto the pan and the chopped garlic. Saute for 2 minutes.
Add the chicken stock, ½ cup of reserved pasta water (save the other half cup if you want to thin out the sauce later) and the heavy cream or half and half. Bring the sauce to a simmer, reduce the heat to medium-low, and add the parmesan cheese. Continue to simmer the sauce for 3 more minutes to incorporate.
Combine:
Add the cooked pasta and stir to combine with the sauce. If it’s too thick, slowly add a little more of the reserved pasta water to thin it out to a consistency of your liking.
Slice the chicken breasts into slices and toss into the pasta right before serving.