Quick-pickle the carrot: toss the matchsticks with 1 tablespoon of the rice vinegar, the sugar and a pinch of salt. Set aside while you cook the fish.
Whisk the soy sauce, remaining tablespoon of rice vinegar, sesame oil, ginger and honey in a small bowl to make the dressing.
Pat the salmon dry and season lightly with salt. Heat the oil in a nonstick or well-seasoned skillet over medium-high heat. Add the salmon, skin side down if it has skin, and cook without moving for 4–5 minutes until the bottom is golden.
Flip and cook 2–4 minutes more, until the thickest part flakes easily and reaches 145°F (63°C). Transfer to a plate and break into large flakes, discarding the skin if you like.
Divide the warm rice between two bowls and drizzle with a spoonful of the dressing. Arrange the salmon, cucumber, avocado and drained carrot on top.
Sprinkle with green onions, sesame seeds and nori. Serve the remaining dressing on the side.