Prepare the garlic: Cut garlic cloves in half, smash to remove papers, then chop until a small dice. Add coarse salt and use the flat blade of your knife to chop and smash the garlic until it forms a paste, with small dice remaining. Place in a bowl and set aside.
Prepare the parsley: Roll up a small bundle of fresh Italian Parsley, slice as finely as possible, then chop in every direction until processed into a fine mince. Place in a bowl and set aside.
Prepare the lemon: Slice half of the lemon into thin rounds and remove the seeds. Save the other half for its juice.
Make the Beurre Manié: Take 1 tablespoon of softened Unsalted Butter and knead it into 1 tablespoon of All-Purpose Flour until the flour is completely incorporated and you can't tell it was ever there. Place back into the fridge until ready to use.
Prepare the breading station: Set up two stations – one with All-Purpose Flour and one with beaten eggs. Season both the flour and the beaten eggs with a little Italian Oregano and coarse salt.
Slice the chicken: Using a thin boning knife, carefully shave thin slices of Boneless Skinless Chicken Cutlets (thinly sliced) from the thicker side of the filet, making them as thin as possible. Lay the pieces out on a board and season them on both sides with coarse salt.
Dredge the chicken: First, dredge each chicken slice into the seasoned flour, shaking off any excess. Then, drop it into the seasoned beaten egg, ensuring it's well coated. Hold the cutlets in the egg until ready to cook.
Cook the chicken: In a high-rimmed sauté pan, add enough olive oil to coat the bottom and heat until hot. Add chicken cutlets, about three at a time. Cook hard and fast on one side until nicely browned and about 60% cooked, checking the edges for browning. Flip and cook briefly on the other side, just to kiss with heat, until 85–90% cooked. Remove from pan and transfer to a plate. Repeat with remaining chicken, rotating them while cooking for better browning. Set aside.
Prepare the sauce base: Drain the oil from the pan and let the pan cool slightly if overheated. Add a small amount of fresh oil, then add the prepared garlic. Cook on medium-high until the garlic is nicely browned and fragrant. Turn off the heat and deglaze the pan with White Wine. Return to heat and reduce the wine until lots of small bubbles appear.
Reduce the stock: Add about 3 cups of Chicken Stock to the pan. Bring to a simmer and allow the sauce to reduce by about halfway, until it starts to form a tiny bit of structure (gauge by swirling in the pan).
Add lemon and Beurre Manié: Once reduced, add the lemon slices. Juice the reserved half lemon through a strainer into the sauce to catch seeds. Season with coarse salt. Take the kneaded Unsalted Butter (Beurre Manié) from the refrigerator and slowly toss it into the sauce, working it in until completely melted. Bring the mixture back to a boil to activate its thickening power; the sauce will thicken in real time.
Finish cooking the chicken: Add the cooked chicken cutlets back to the pan, along with any accumulated cooking juices. Let the sauce cook for about 2–3 minutes with the chicken to finish cooking the chicken and allow it to become tender and juicy. The sauce should hold the back of a spoon.
Adjust and serve: Taste the sauce for balance. If too lemony, add more Unsalted Butter. If too thick, add a little more Chicken Stock. Finish with fresh Italian Parsley. Shingle the chicken around the center of a plate, place lemon wedges on top, and spoon a generous amount of sauce over the chicken and around the plate. Serve hot, ideally with fresh bread for sopping up the sauce.
