Season salmon with salt + pepper. Cook salmon fillets in oil over medium-high heat, skin side up, for 5 min. Flip the filet and cook for another 4 min. Cook salmon until internal temperature reads 145° F on a food thermometer.
At the last minute, brush the honey mustard mixture evenly over the salmon fillets. Serve salmon with arugula, rice, and/or any remaining honey mustard sauce.