Remove the salmon from the refrigerator and let sit at room temperature for 10 minutes.
In a small saucepan, melt 1 teaspoon of butter over medium heat, then add the minced garlic and sauté until lightly golden, about 1–2 minutes.
Pour in the chicken broth and lemon juice and simmer until reduced by half to about 3 tablespoons, about 3 minutes.
Remove the pan from heat, whisk in the remaining 3 tablespoons of diced butter and the honey until smooth, then set the sauce aside.
Pat the salmon dry on both sides with paper towels and season both sides with salt and freshly ground black pepper.
Heat the olive oil in a 12-inch nonstick skillet over medium-high heat until shimmering.
Add the salmon fillets, presentation-side down, and cook without moving until the bottom is golden brown, about 4 minutes.
Flip the fillets and cook until opaque and cooked through, about 2–3 minutes more depending on thickness.
Transfer the salmon to plates, drizzle each serving generously with the garlic lemon butter sauce, sprinkle with minced parsley, and garnish with lemon slices if desired. Serve immediately.