Heat 1 tablespoon of coconut oil in a large skillet over medium-high heat. Add the carrots and season with salt and pepper, to taste. Cook, stirring, until they begin to soften, about 3 minutes. Remove from skillet and set aside.
Add the remaining 2 tablespoons of coconut oil to hot skillet, and add in bell peppers, mushrooms, and onions. Cook again, stirring, about 5 minutes. Add in garlic and season with salt and pepper. Cook 30 seconds longer. Remove from skillet and set aside with carrots.
Add honey and coconut aminos to the skillet and heat on low until warm and combined. Add the noodles, cooked vegetables, and spinach to sauce and toss with sesame oil.
To serve, garnish with sliced green onions and sesame seeds. Serve either warm or cold.