Cut the chicken breasts in half horizontally. Use a meat mallet to pound down the thicker pieces on the chicken breasts. This will ensure even cooking and browning.
In a shallow bowl combine flour, 5 tbsp finely grated parmesan cheese, garlic salt, and ground black pepper. Dredge chicken in the flour mixture, making sure to shake off excess flour.
In a large skillet over medium-high heat add olive oil and butter. Add chicken breasts and let cook 5-6 minutes on each side until evenly browned. Flip each breast over and continue to brown on the other side. Cook until no longer pink and the chicken is 165 degrees inside when checked with a meat thermometer. Remove chicken to a plate and set aside.
Reduce heat to medium and add onions to the remaining juices and oil in the pan. Cook for 5 minutes stirring often. Add minced garlic to the pan and allow to cook 2-3 additional minutes stirring often.
Add chicken broth to the skillet and use your spoon to deglaze the bottom of the pan. Make sure to get all of the brown bits up into the sauce. Reduce heat to medium-low and allow it to simmer for 5 minutes.
Pour in the heavy cream and stir well. Simmer on medium-low heat for 3 minutes. Add Parmesan cheese and additional garlic salt. Stir to combine. If your sauce is too thin you can put 3 tsp cornstarch into a small bowl and add 3 tsp of the garlic cream sauce. Use a fork to mix together. Add to the garlic cream sauce and stir well. Let simmer an additional 2-3 minutes, stirring often.
Add the chicken back to the pan and let it sit in the simmering sauce until it comes back up to temperature.
Serve over rice, mashed potatoes, pasta, or cauliflower mash. Use the sauce as gravy and garnish with parsley.