In a small bowl, whisk together the honey, soy sauce, and lemon juice. In another small bowl, mix the cornstarch with water until smooth. Set both mixtures aside.
Pat the salmon fillets dry with paper towels. Season both sides with salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat. Place the salmon skin-side down if using skin-on fillets. Cook for 4–5 minutes without moving the fish, then carefully flip and cook for another 3–4 minutes. Transfer the salmon to a plate.
Reduce the heat to medium. Melt the butter in the same skillet, then add the minced garlic and cook for about 30 seconds until fragrant.
Pour the honey mixture into the skillet and stir well. Whisk in the cornstarch slurry and cook for 2–3 minutes until the glaze thickens.
Return the salmon to the skillet and spoon the glaze over each fillet. Cook for another 1–2 minutes until the salmon reaches an internal temperature of 145°F (63°C) and flakes easily with a fork.
Garnish with chopped parsley and serve immediately with rice, roasted vegetables, or mashed potatoes.