Preheat oven to 400 degrees and prepare a baking sheet with foil. Thoroughly rinse produce and pat dry. Trim ends off green beans. Trim ends off carrots, peel, and cut into 1/2" pieces at an angle. Zest and quarter lemon. Reserve two quarters for garnish and juice other quarters. Rinse trout, pat dry, and season with a pinch of salt and pepper.

Combine carrots with 1/4 cup water and 1 Tbsp. butter in a medium pan over medium-high heat. When water begins to steam, cover pan, reduce heat to medium, and cook 5-6 minutes until carrots are tender and lightly glazed. Season with smoked salt and a pinch of pepper.

Place green beans on prepared baking sheet, drizzle with 1 tsp. olive oil, and season with a pinch of salt and pepper. Roast 7-9 minutes until tender and slightly caramelized.

While carrots steam, heat 1 tsp. olive oil in a medium non-stick pan over medium-high heat. Add trout, skin-side up, and sear 4-5 minutes until well-browned. Carefully flip trout and cook 4 more minutes or until trout reaches a minimum internal temperature of 145 degrees. Remove trout, skin side up, to a plate and allow to rest. Wipe pan clean and return to heat.

Over medium heat, toast almonds in dry pan 1-2 minutes. Stir constantly until golden brown. Remove from pan. Add remaining butter to pan and melt. When it begins to turn brown and smell nutty, remove pan from heat. Butter browns shortly after it stops sizzling, so listen closely when it's ready. Add white cooking wine and 2 tsp. lemon juice. Return to heat, bring to a boil, and cook 1-2 minutes, until sauce reduces slightly. Remove pan from heat and stir in almonds.

Reheat sides over medium heat if necessary. Place a serving of beans and carrots on plate. Lift corner of trout skin and gently peel, carefully using a knife to loosen skin. Place trout on plate, skinned side down. Serve trout in front and top with brown butter-almond mixture. Garnish liberally with lemon zest and serve remaining lemon on the side.