Start the rice: Make the rice first and keep warm in the rice cooker while you prepare the rest of the recipe.
Make the salsa: Combine the 1 diced mango, the minced jalapeño, the minced 1/4 red onion, the 1/4 cup chopped cilantro, the 1/4 cup fresh lime juice, and 1/2 teaspoon salt in a medium bowl. Stir to combine.
Season salmon: Combine the 2 teaspoons chili powder, 1 teaspoon garlic powder, 1 teaspoon salt, and 1/4 teaspoon pepper in a small bowl. Drizzle the salmon all over with 1 tablespoon of the olive oil the sprinkle the spice mix over the top of the salmon. Rub it in well.
Cook the veggies: Heat 1 tablespoon of the olive oil in a large skillet over medium-high heat. Add the 2 sliced peppers and 1/2 pound trimmed green beans and season with 1 teaspoon salt and 1/2 teaspoon pepper. Cook, stirring ocassionally, until crisp tender and lightly charred in spot, about 5 minutes. Remove to a plate. If skillet is really charred on the bottom, remove from stove and wash it out before cooking the salmon.
Cook the salmon: Heat the last tablespoon of olive oil in the skillet over medium-high heat and add the salmon fillets, skin-side up. Cook, undisturbed until golden brown and the flesh has become opaque about halfway up the side of the salmon, about 2 minutes. Flip and crisp the skin on the other side, another 2 minutes. The fish doesn't have to be completely cooked, it will continue cooking in the garlic butter sauce. Remove to a plate, peel off the skin and discard if you'd like.
Make garlic sauce: Return the skillet to medium heat and add the 3 tablespoons butter and 2 cloves of sliced garlic. Let cook until butter has melted and garlic is fragrant. Add 1/4 cup lemon juice, 1 tablespoon brown sugar, 1/2 teaspoon kosher salt, and 1/4 teaspoon black pepper and bring to a simmer, then reduce heat to low. Slide salmon fillets back in the sauce and cook until the salmon is done to your likeness. I like mine cooked to about 125°F, about 1-2 minutes more.
Serve: Stir lime zest and chopped cilantro into the rice. Spoon the rice into bowls and place a salmon fillet in each bowl. Add the veggies to each bowl and spoon the butter sauce over the salmon. Top each bowl with mango salsa and serve.