Place cucumber & carrot in a medium bowl. Season with 2 tsp salt & stir to combine well. Let stand for 15-20 minutes. Rinse the vegetables well, draining any excess water, & use paper towel to pat the vegetables as dry as possible. Meanwhile, combine the sugar & rice vinegar in a small bowl, seasoning with 1/4 tsp salt. Microwave 30 seconds. Pour pickling liquid over the seasoned cucumber & carrot. Mix gently to combine. Cover & chill before serving.
Meanwhile, as the pickled veggies soak, prepare the salmon. Add the brown sugar, soy sauce & mirin to a medium bowl. Stir to combine well. Transfer half of the marinade to a small bowl & reserve for serving. Add the cubed salmon & sliced green onion to the medium bowl with the marinade. Stir to coat. Set aside to marinate for 20-30 minutes.
Add oil to a medium skillet over medium-high heat. Once the oil is hot & shimmering, add the salmon to the skillet, shaking off & discarding any excess marinade. Cook 2 minutes, then flip & cook 90 seconds - 2 minutes longer, or until your desired doneness is reached. Work in batches as necessary & resist the temptation to mess with the salmon as it cooks to ensure you achieve a beautiful golden sear. Transfer the seared salmon to a plate & set aside for serving.
Add rice to a large, shallow bowl, then top with the namasu vegetables & seared salmon. Drizzle some of the reserved soy marinade over top. Finish as desired with a generous sprinkling of furikake (Japanese nori seasoning), toasted sesame seeds, &/or thinly sliced green onions.