Prepare the Salmon: Combine flour, garlic powder, salt, and black pepper in a large shallow dish. Coat each salmon fillet with this mixture and set them aside after giving them a gentle shake.
Sear the Fillets: Heat olive oil in a large non-stick pan over medium-high heat until hot. Carefully add the coated salmon fillets and fry for about 3 minutes until they develop a golden crust on one side before flipping them over gently.
Baste with Butter: Fry the other side of the salmon for an additional 2 minutes until golden brown as well. Add in 1 tablespoon of butter during this step and baste the fillets continuously until they are nearly cooked through before removing them from the pan.
Create the Sauce: Lower heat to medium and add finely diced garlic to the same pan, frying until it starts to take on color without burning. Pour in vegetable stock while scraping up any flavorful bits stuck on the bottom of the pan.
Whisk in More Butter: Add in the remaining chunks of unsalted butter and whisk thoroughly until combined with stock, creating a smooth and cloudy sauce. Stir in parsley along with additional salt and pepper if desired.
Finish Cooking & Serve: Allow sauce to simmer gently while stirring occasionally until it thickens slightly before returning salmon fillets back into the pan. Baste them again in that luscious sauce just before serving along with lemon wedges for an extra burst of flavor.