In a small bowl, whisk together the light brown sugar, Dijon mustard, lemon zest, and minced garlic until well combined.
Pat the salmon fillets dry with paper towels. Season both sides generously with salt and freshly ground black pepper.
Place your non-stick skillet over medium heat and allow it to warm up.
Once the skillet is hot, place the salmon fillets in the pan, skin side down if applicable. Cook for about 4-5 minutes.
Carefully flip the salmon fillets over and pour the brown sugar glaze over the top of each fillet. Let it bubble and caramelize for another 3-4 minutes.
Once the salmon is cooked through, remove it from the skillet and sprinkle with chopped fresh parsley, if using. Serve immediately.
