Preheat the oven to 375 degrees F (190 degrees C).
Combine 1/2 cup olive oil, lemon juice, garlic, brown sugar, oregano, thyme, salt, and pepper in a bowl.
Place a large piece of aluminum foil on a baking sheet and brush with olive oil. Place salmon in the middle of the foil, skin-side down. Drizzle with olive oil mixture. Fold up the edges of the foil over the salmon to create a packet, making sure to seal the edges.
Bake in the preheated oven until fish flakes easily with a fork, 20 to 25 minutes. If your salmon fillet is very thick, it can take longer. Garnish with fresh parsley and lemon slices.
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