Pat the salmon fillets dry with paper towels, and season both sides with sea salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat. Once hot, place the salmon fillets skin-side down in the skillet. Cook for 4 minutes until the skin is crispy.
Carefully flip the salmon fillets and cook for an additional 2-3 minutes, or until the desired doneness is reached. Remove the salmon from the skillet and set aside.
In the same skillet, reduce heat to medium and add the minced garlic. Sauté for 1 minute until fragrant.
Add the sliced piquillo peppers to the skillet and sauté for another 2 minutes.
Pour in the white wine and vegetable broth, and bring the mixture to a simmer. Let it cook for 3 minutes, allowing the sauce to slightly reduce.
Stir in the fresh parsley, lemon zest, and lemon juice, and cook for another minute.
Return the salmon fillets to the skillet, spooning the piquillo pepper sauce over them. Heat through for 1 minute.
Serve the salmon fillets with the sauce spooned over the top, garnished with additional parsley if desired.