Slice chicken breasts into 4 thin filets. Mix flour, salt, and pepper in a shallow bowl, and dredge each chicken filet in the four, making sure to evenly coat both sides. Shake off excess, and set aside.

Heat oil and butter in a large skillet over medium high heat. Cook the chicken until golden brown and cooked through, about 2-4 minutes per side, depending how thick the chicken is. Remove chicken from pan, and set aside.

To make the sauce, add the garlic into the skillet, and cook for about 1 minute. Reduce heat to low-medium, add the broth and milk. Bring the sauce to a boil; season with salt and pepper.

Stir in parmesan cheese and capers and let simmer for about 2 minutes until it gets a little thicker. Then mix the cornstarch with 1 tbsp of water, and whisk it into the sauce.

Now stir in the lemon juice, then return the chicken to the pan. Let warm a minute, then serve.