For best flavor and texture, look for large curly-leafed spinach leaves rather than baby spinach in the clamshell container.
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.