Start by cooking the pasta according to package instructions in a large pot of salted water. While the pasta is boiling, slice the chicken breasts into bite sized pieces, then coat them in the Cajun spice. You can use store bought seasoning or make mix your own using my recipe. (link in the ingredient list)
Heat the olive oil in a large pan and cook the seasoned chicken over medium heat until done all the way through, which will take approximately 5-7 minutes depending on the thickness of the pieces. Remove to a separate plate.
Lower the heat to low. To the same pan add the butter and let it melt, then 1 clove of grated or pressed garlic and cook for 30 seconds without allowing it to burn, add the double/heavy cream and let it heat for about 5 minutes, then sir the grated Parmesan and allow the cheese to melt slowly into the sauce, continue stirring until the sauce comes together, then take it off the heat. Grate the nutmeg directly into the sauce, just a few gratings will do.
Drain the pasta and reserve ½ cup of the pasta water, add the pasta to the pan with the sauce together with the cooked chicken. Toss gently to combine, season with salt to taste, add a splash of the reserved pasta water to loosen the sauce if it gets too thick.