Pat salmon fillets completely dry with paper towels. Season both sides generously with salt and pepper.
Heat olive oil in a large skillet over medium-high heat until shimmering. Carefully place salmon fillets in pan, leaving space between each.
Cook undisturbed for 4-5 minutes until deep golden crust forms on bottom. Flip gently and cook another 3-4 minutes until almost cooked through (125°F internal).
Remove salmon to a plate and tent with foil. Reduce heat to medium, add 2 tablespoons butter to same pan.
Add minced garlic and cook 30 seconds until fragrant. Stir in honey, lime juice, and lime zest. Whisk constantly 1-2 minutes until sauce thickens slightly.
Remove from heat and whisk in remaining tablespoon butter. Pour sauce over salmon fillets. Garnish with parsley and serve with lime wedges.