Season chicken breasts with lemon pepper seasoning and salt on all sides. Coat in the flour.
Heat a skillet over medium-high heat and add 1 tbsp butter and 1 tbsp oil. Cook 2 chicken breast halves in skillet till golden brown on each side, about 3 to 4 minutes until cooked through. Remove from pan to a plate to keep warm.
Add another tablespoon of butter and a tablespoon of oil to the pan and cook the remaining two chicken breasts. Remove from pan and keep warm.
For the Sauce:
To the pan melt 3 tbsp butter and add in the garlic, cooking until fragrant, about 30 seconds. Whisk in the flour, until smooth. Splash in the white wine, scraping any browned bits off the bottom of the pan and cook until the wine is evaporated. Gradually pour in the chicken stock, whisking until mixture is smooth. Add the lemon juice and capers to the sauce and allow to simmer until reduced slightly (about 5 minutes).
Finally add in the remaining tablespoon of butter and let it melt into the sauce. Add the chicken breasts back to the skillet and let simmer for an additional 5 minutes to heat through. Garnish with fresh parsley and lemon wedges if desired. Serve immediately over freshly cooked pasta and enjoy!