In a small pot, heat 1 tablespoon of the neutral oil over medium heat until warmed. Add the garlic and ginger and cook until fragrant and softened, about 1 minute. Add the rice and 1¾ cups water, cover, and cook until the rice is tender and the water is absorbed, about 45 minutes. Remove the pot from the heat and let the rice stand, covered, for 5 minutes.
Meanwhile, in a small bowl, whisk together the soy sauce, honey, rice vinegar, and sesame oil. Set the teriyaki sauce aside.
About 15 minutes before the rice is done, in a large skillet, heat the remaining 1 tablespoon neutral oil over medium-high heat until shimmering. Season the salmon lightly with salt and add to the pan skin side down. Cook until the skin is browned and crisp, about 4 minutes. Flip and cook for 1 minute, so the fish is not yet cooked through. Transfer to a plate.
Pour the oil out of the skillet and wipe it clean. Add the teriyaki sauce and bring to a boil over medium-high heat. Cook until the sauce is reduced by half, about 1 minute. Return the salmon to the skillet, skin side up. Tip the skillet so the sauce pools and spoon it over the salmon and cook until the sauce is syrupy and the salmon is just cooked through, about 2 minutes. Remove the skillet from the heat.
Fluff the rice and divide among four bowls. Top with the salmon, cucumber slices, and avocado. Serve, garnished with sesame seeds and scallion greens if desired.