Peel and finely chop carrot. Finely chop celery and onion. Mince garlic.
In a large pan over medium heat, saute the carrots, celery, and onion in a swirl of olive oil until translucent, about 5-8 minutes.
Add the garlic, and cook for 30 seconds.
Add the ground turkey and break it up with a spoon. Increase the heat to medium-high and cook, stirring often, until the turkey is no longer pink.
Add the tomato sauce, vinegar, mustard, honey, and chili powder to the pain. Stir well to combine, then cover and simmer for 5 minutes.
Remove the lid, and simmer five minutes more, uncovered, until the sauce is thickened and flavorful.
Add salt and pepper to taste, then spoon the hot filling onto whole wheat buns, and serve.