Prepare the sauce by melting 1 teaspoon butter in a heavy saucepan over medium heat.
Add the garlic and saute until lightly golden brown, about 1 to 2 minutes.
Add the chicken broth and lemon juice. Simmer until reduce in half, about 3 to 4 minutes.
Add the remaining 3 tablespoons butter and honey, and whisk until the butter is melted and incorporated. Remove from the heat and set aside.
Rub salmon fillets on both sides with the olive oil and then season with salt and pepper.
Place the salmon on a hot grill pan, and cook for 4 minutes, or until golden.
Gently turn over and cook the other side for another 2 to 3 minutes or until just cooked through.
Remove from the heat and rest for a while. Drizzle the salmon fillets with the sauce, sprinkle with the parsley and garnish with the lemon slices, if desired.