Season the chicken with salt and pepper on both sides then dredge the cutlets in flour and shake off the excess. Place the dredged cutlets on a parchment paper lined baking sheet.
Heat a large nonstick pan to a touch less than medium heat, then add 1 tablespoon of olive oil and butter to the pan. Sear the chicken cutlets until cooked through (approximately 3-4 minutes per side) then set aside on a platter lightly tented with foil. Do not crowd the pan. Work in batches, using a bit more olive oil and butter as required for each batch.
Using the same pan, turn the heat to low and add the garlic and a touch more olive oil. Saute until golden (about 1-2 minutes) then add the capers and cook for 1 minute more.
Add the wine and chicken stock to the pan and turn heat to high. With a wooden spoon dislodge all the brown bits from the bottom of pan. Boil for 1-2 minutes then add the lemon slices, lower the heat, and simmer for another 2 minutes.
Roll the remaining butter cubes in the leftover flour and shake off the excess. Add one cube at a time to the pan. Using a whisk or wooden spoon, stir the sauce to emulsify. Taste test the sauce and adjust salt, pepper, and lemon juice levels if required.
When satisfied with the taste of the sauce, add the chicken and half the parsley and gently coat all the pieces. Cook for 2-3 minutes to warm through. Turn off heat and add the remaining parsley. Serve with remaining lemon wedges. Enjoy!