Bring chicken broth and butter to a boil in a saucepan. Add rinsed brown rice and reduce heat to medium-low. Cover and simmer until rice is tender and liquid has been absorbed, 45 to 50 minutes. When finished, remove from the heat, cover, and keep warm.
Meanwhile, preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper.
When the rice has about 30 minutes left, combine green beans, sweet potato, olive oil, salt, and pepper in a bowl; toss to combine. Transfer to the prepared baking sheet, separating green beans on one side and sweet potatoes on the other.
Combine honey, chipotle pepper, and garlic in a bowl; season to taste with salt and pepper. Brush mixture onto frozen salmon and place on top of the green beans, skin-side down (this step is important.)
Roast in the preheated oven until vegetables are soft and salmon flakes easily with a fork, 30 to 35 minutes.
Remove from the oven. Divide rice between 2 bowls. Top each bowl with vegetables and a salmon fillet. Sprinkle toasted pecans over top.