Halve chicken breasts and season both sides with salt and lemon pepper seasoning.
Heat a cast iron skillet or large saute pan to medium-high and melt 2 tablespoons of butter and 1 tablespoon of olive oil.
Add seasoned chicken to the pan. Cook chicken for 4 minutes on one side and 4-5 minutes on the other, turning the heat down to medium until the internal temperature of then chicken reaches at least 165 degrees.
Remove chicken from pan and set aside. Add final 2 tablespoons of butter and garlic and saute. Add chicken stock and lemon juice to the pan to deglaze the pan.
Whisk in flour and cook for another 2-3 minutes until it thickens. Add sliced lemon to the pan, if preferred.