Blot the salmon fillets dry with paper towels. Season them with salt, pepper, garlic powder, and dried thyme.
Heat a large (12-inch) cast-iron skillet over medium-high heat. Add the olive oil and butter and swirl to coat. You can also use a nonstick skillet.
When the butter starts foaming, add the salmon fillets, skin-side-down. If using, add the lemon slices.
Cook the salmon, undisturbed, until the skin is crispy and browned, for about 4 minutes. Flip the salmon and lemon slices, lower the heat to medium, and continue cooking for 3 more minutes.
If your fillets are 1 inch thick, cook the edges for about 2 minutes per side. This helps ensure the salmon reaches an internal temperature of 145ºF.
Transfer the salmon fillets to a serving plate and drizzle them with the pan juices. Garnish the plate with lemon slices and chopped parsley, and serve.
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Notes
If your salmon is frozen, thaw it thoroughly before using it in this recipe. You can thaw it overnight in the fridge.
You can skip the olive oil and use two tablespoons of butter. The butter's milk solids have a blackening effect, making the salmon extra-crispy.
The best skillets for this recipe are nonstick or well-seasoned cast-iron skillets. I don't recommend using a stainless steel skillet - the salmon skin tends to stick to it.
Don't forget to drizzle 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 an airtight container in the fridge 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.