Preheat oven to 400°F. Stir 1½ tablespoons honey and the grated garlic together in a small bowl until well combined.

Heat 1 tablespoon oil in a large oven-safe skillet over medium-high heat. Brush tops of 4 salmon fillets with 1½ teaspoons honey mixture; reserve the remaining 1½ tablespoons honey mixture. Place the salmon in the hot skillet, honey-side down; cook, undisturbed, until deeply browned, 1 to 2 minutes. Transfer to a plate, browned-side up; do not wipe the pan clean.

Add 4 cups broccoli, chopped bell pepper, sliced scallions, sliced carrot, ¼ teaspoon pepper, ¼ teaspoon salt and the remaining 1 teaspoon garlic to the skillet; cook over medium heat, stirring often, until the vegetables begin to soften, about 2 minutes. Stir in 2½ tablespoons soy sauce and 1 tablespoon vinegar and scrape up any browned bits on the bottom of the pan. Stir in 1 package rice and ¼ cup broth.

Transfer to the oven and bake, uncovered, until the broccoli is almost tender, about 10 minutes. Remove from the oven; brush the top and sides of the salmon evenly with the reserved honey mixture and sprinkle with the remaining ¼ teaspoon salt. Nestle the salmon into the broccoli mixture, browned-side up. Bake, uncovered, until an instant-read thermometer inserted into the thickest portion of salmon registers 120°F, 6 to 8 minutes. Garnish with scallions, if desired.