Blot the salmon fillets dry with paper towels. Season them with salt, pepper, garlic powder, and dried thyme.
Heat the olive oil and butter in a large (12-inch) nonstick skillet over medium-high heat, swirling to coat.
When the butter starts foaming, add the salmon fillets to the pan, skin-side-down. If using, add the lemon slices, too.
Cook the salmon, undisturbed, until the skin is crisp and browned, for about 4 minutes.
Flip the salmon and lemon slices, lower the heat to medium, and continue cooking for 3 more minutes. Then, if your fillets are ½ inch thick or more, cook the edges for about 2 minutes per side. The salmon's internal temperature should reach 145ºF.
Transfer the salmon to a plate and baste it with the pan juices. Top each fillet with a lemon slice, sprinkle with chopped parsley, and serve.
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Notes
If your salmon is frozen, defrost it thoroughly before using it in this recipe. You can thaw it overnight in the fridge.
Don't forget to drizzle (or brush) the salmon with the pan juices after you've arranged it on the plates. The pan sauce is delicious.
You can keep the leftovers in the fridge, in an airtight container, for up to three days. I prefer to avoid reheating them because reheating can dry them out and make them taste fishy. Instead, I crumble them cold over a salad.