Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper.
In a small bowl, whisk together brown sugar, soy sauce, Dijon mustard, olive oil, and garlic.
Place salmon fillets on the prepared baking sheet, skin side down. Season lightly with salt and pepper.
Brush the glaze generously over each fillet, letting it drip down the sides.
Bake for 12-15 minutes, depending on the thickness of your salmon, until it flakes easily with a fork.
Switch to broil for the last 1-2 minutes if you’d like a caramelized top.
Sprinkle with fresh parsley and serve with lemon wedges.