Preheat oven to 450 degrees. Whisk together soy sauce, vinegar, Dijon, honey, and oil. Season with salt and pepper. On a rimmed baking sheet, toss mushrooms with 2 tablespoons dressing. Roast, stirring once, until browned, about 15 minutes. Remove from oven; add spinach, carrots, and remaining dressing directly to hot baking sheet. Season with salt and pepper, toss to coat, and serve.