Preheat the oven to 375 degrees F (190 degrees C).

Combine 1/2 cup olive oil, garlic, lemon juice, brown sugar, oregano, thyme, salt, and pepper in a bowl.

Place a large piece of aluminum foil on a baking sheet and brush with 1 teaspoon olive oil. Place salmon, skin-side down, in the middle of the foil. Drizzle with seasoned olive oil mixture.

Fold up the edges of the foil over 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. Garnish with fresh parsley and lemon slices.