Press salmon fillets between paper towels to dry surfaces thoroughly. Season on all sides with salt and pepper.
Heat oil in a large stainless steel skillet over medium-high heat until shimmering. Add salmon fillets, skin side down. Immediately reduce heat to medium-low. Cook, pressing gently on back of fillets to ensure good contact between the skin and the pan, until skin is rendered and crisp, about 6 minutes.
Flip salmon and cook on second side until a thermometer inserted into the thickest part registers 120°F or medium-rare or 130°F for medium, about 1 minute longer. Transfer salmon to a paper towel lined plate to drain.
Divide the coconut rice evenly between 4 bowls.
Top with diced avocado, cucumber, seaweed, edamame and scallions. Top each bowl with a salmon fillet and spoon sauce on top and evenly glaze each fillet.
Sprinkle with furikake and sesame seeds.
Serve immediately.