Start by mixing the flour with garlic powder, salt, and black pepper in a shallow dish. This seasoned flour does double duty, adding flavor while also giving the sauce something to cling to later. Give it a quick stir so everything's evenly distributed before you start coating the chicken.
Butterfly each chicken breast right through the center so you end up with four thinner, even-sized pieces. Thinner chicken cooks faster and more evenly, which matters a lot here. Press each piece into the flour mixture on both sides, then shake off any excess before setting it aside.
Heat a tablespoon each of butter and olive oil in your pan over medium-high heat. Once it's hot, lay the chicken in and fry until golden on both sides and cooked through, roughly 3 to 5 minutes per side. Transfer the chicken to a plate and set it aside while you build the sauce.
Turn the heat down to medium and add your minced garlic to the same pan. Let it cook for a minute or two until fragrant, then pour in the chicken stock and scrape up any browned bits stuck to the bottom. Those little bits are pure flavor, so don't skip this part.
Add the remaining butter to the pan in small chunks, whisking constantly as it melts into the stock. This step, called emulsifying, is what turns the liquid into a silky, slightly thickened sauce rather than a greasy puddle. Keep whisking until everything looks smooth and glossy.
Stir in the chopped parsley and season the sauce with salt and pepper to taste. Let it simmer gently for a few minutes so it thickens slightly and the flavors meld together. You'll notice the sauce clinging nicely to the back of a spoon when it's ready.
Lower the heat and nestle the chicken back into the pan, spooning the sauce generously over each piece. Let it warm through for a minute, then serve immediately with a lemon wedge on the side. Don't let it sit too long in the pan or the chicken can overcook.