Season both sides of your salmon fillets with salt and black pepper. Set aside. Combine olive oil and butter in a large skillet. Place the skillet over a stove burner set to medium-high heat. Heat the skillet until the butter melts and starts sizzling.
Place the salmon fillets in the skillet. Pan sear the salmon for about 3 to 4 minutes, or until golden brown on one side. Flip, and sear the other side for another 1 to 2 minutes, or until golden brown. It's ok if the salmon isn't cooked through yet! Transfer the salmon to a plate, and set aside.
Discard any excess butter/oil in the skillet. Add your garlic, honey, soy sauce, and water to the skillet. Place the skillet over medium heat until the sauce is warmed through and the honey is dissolved.
Return the salmon to the skillet. Cook over medium heat, occasionally basting the salmon with the honey garlic sauce, until the salmon is fully cooked through. Add your lemon juice, and (if using) sesame seeds and chives. Serve!