Slice 6 lemon rounds; set aside with both lemon halves.
In shallow bowls, set up flour and egg wash (eggs + milk).
Drench chicken in flour, then egg.
Heat oil over medium; cook chicken 2–3 minutes per side. Remove and set aside.
Wipe skillet clean; melt 2 tbsp butter. Sauté lemon halves and slices for 1–2 minutes; remove slices.
Add shallot and cook 2–3 minutes. Add garlic for 45 seconds.
Stir in 2 tbsp flour; cook 1 minute.
Add wine, chicken stock, salt, and pepper. Simmer 4–6 minutes to thicken.
Add 1 tbsp butter and lemon juice. Stir to combine.
Return chicken to pan, coat with sauce, and top with lemon slices and parsley.
Serve with your favorite side like mashed potatoes, rice, polenta, or pasta.