Combine the Cajun Rub spices together. Set aside.
Flatten the thickest part of the chicken breasts, if necessary, to help with even cooking. Season both sides of the chicken with the Cajun Rub.
In a shallow skillet, heat the oil over medium heat. Once the oil is hot, sauté the chicken breasts on both sides to cook evenly and through, (reading 165 degrees temp on a digital thermometer), about 3 to 5 minutes per side, depending on the thickness of the chicken and the heat of your stovetop. Remove to a plate to keep warm.
Wipe out the skillet (or you can use a different skillet) and return to the heat. Melt the butter over medium heat.
Once the butter is melted, add the garlic and sauté for 30 seconds, stirring constantly.
Add the heavy cream, stock, and nutmeg. Stir over medium heat to warm through.
Add the cheese and stir until it is melted and the sauce is well combined.
Taste for seasoning and add salt as desired.
Add the pasta to the sauce and stir to coat evenly.
Slice the chicken into strips.
To serve, divide the pasta between bowls. Top each bowl of pasta with sliced chicken. Sprinkle with parsley, if desired. Serve warm.