Bring 3/4 cup water and a pinch of salt to a boil in a medium, lidded pot. Bring 2 TBSP butter to room temperature. Wash and dry all produce. Trim and thinly slice scallions. Peel and mince or grate ginger. Chop cilantro. Quarter lime. Trim and peel carrots, then cut diagonally into 1/2-inch-thick slices.

Once water is boiling, add rice to pot. Cover and reduce heat to low. Cook until tender, 12-15 minutes. Keep covered until ready to serve.

While rice cooks, pat chicken dry with paper towels; season all over with salt and pepper. Heat a large drizzle of olive oil in a large pan over medium-high heat. Add chicken and cook until browned and cooked through, 3-5 minutes per side.

Meanwhile, in a medium bowl, combine scallions, sesame oil, 1 tsp sugar, 1 TBSP olive oil, half the ginger, juice from 2 lime wedges, and sriracha (to taste). Season with salt and pepper. Taste and add more ginger or lime juice, if desired. In a small bowl, combine 1 TBSP softened butter and remaining ginger.

In a medium microwave-safe bowl, combine carrots and a splash of water. Cover with plastic wrap. Poke a few holes in the plastic wrap and microwave until tender, 4-6 minutes. Drain any excess liquid from bowl, then stir in ginger butter and soy sauce (to taste).

Stir cilantro and remaining softened butter into rice; season with salt and pepper. Divide rice and carrots between plates. Top rice with chicken and pesto. Serve with remaining lime wedges on the side for squeezing over.