Dice the onion, bell pepper, carrots, and celery into uniform ¼-inch (6mm) pieces, and mince the garlic cloves finely. Having everything prepped before cooking ensures a smooth process.
Heat olive oil in a large skillet over medium-high heat, then add the ground turkey and cook for 6–8 minutes, breaking it into small crumbles until no longer pink and golden-brown bits form. Season lightly with salt and pepper.
Add the diced onion, bell pepper, carrots, and celery to the pan and cook for 5–6 minutes until softened, then stir in the minced garlic and cook for 1 more minute.
Push the turkey and vegetables to the sides of the pan, add the tomato paste to the center, and cook undisturbed for 1–2 minutes to caramelize it, then stir it into the meat mixture.
Pour in the tomato sauce and chicken broth, then add the coconut aminos, coconut sugar, apple cider vinegar, Worcestershire sauce, and all spices; stir thoroughly to combine and taste to adjust seasoning.
Reduce heat to medium-low and simmer uncovered for 12–15 minutes, stirring occasionally, until the sauce thickens and mounds slightly on a spoon. Add a splash of broth if too thick; continue simmering if too thin.
While the filling simmers, place the halved whole wheat buns cut-side down in a dry skillet over medium heat for 1–2 minutes until golden and slightly crispy.
Remove the skillet from heat, rest for 2–3 minutes, then scoop about ¾ cup of filling onto each toasted bun bottom, add desired toppings, and serve immediately.