Preheat oven to 400 degrees.
After removing salmon from refrigerator, allow to sit on counter until room temperature. This will make the fish tender. Cooking cold fish tends to make it tough.
Rinse room temperature salmon and pat dry with paper towels.
Place salmon fillets on a cutting board. Rub olive oil over all sides of salmon fillets. Set aside.
In small bowl, add brown sugar, smoked paprika (or regular paprika), oregano, thyme, cayenne pepper, ground black pepper, and salt. Stir until well combined.
Use hands to generously coat both sides of salmon fillets with rub.
Warm skillet on top of stove to over medium heat until hot (2-3 minutes). Do not add oil to skillet.
Turn heat off before placing salmon fillets skin-side-down in HOT skillet.
Carefully place skillet in preheated oven for 15 to 20 minutes OR until desired doneness.
When salmon fillets reach desired doneness, remove from oven. Allow to rest 5 minutes.
Before serving, garnish each salmon fillet with chopped parsley (optional).