Prepare the salmon:
Pat the salmon fillets dry with paper towels. Season both sides with salt and pepper.
Make the honey garlic sauce:
In a small bowl, whisk together the honey, minced garlic, soy sauce, Dijon mustard (if using), lemon juice, and grated ginger (if using) until well combined.
Cook the salmon:
Heat the olive oil in a skillet over medium-high heat. Once the oil is hot, add the salmon fillets, skin-side down. Cook for 4-5 minutes on the first side until golden brown.
Flip and glaze:
Flip the salmon fillets over and pour the honey garlic sauce over them. Cook for an additional 3-4 minutes, spooning the sauce over the salmon occasionally, until the salmon is cooked through and flakes easily with a fork.
Serve:
Once the salmon is cooked, remove it from the skillet. Spoon the remaining sauce over the top and serve immediately.