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In a large heavy-bottomed skillet, heat olive oil over medium heat for about a minute. Add turkey, break apart using a wooden spoon, and cook until browned, about ten minutes.
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Add the roughly chopped carrot, celery, and onion to a food processor. Process on low until all the vegetables are finely minced.
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Season the turkey with the salt, pepper, cumin, crushed red pepper flakes, and cayenne. Mix well. Add in the minced carrot, celery, and onion. Cook for five minutes while stirring.
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Stir in the garlic, vinegar, and Worcestershire. Cook for another five minutes.
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Add the tomatoes, ketchup, and tomato paste. Stir to combine. Turn heat to medium/high and bring to a simmer. Simmer mixture for ten to fifteen minutes until it starts to thicken to your liking.
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Cool slightly before serving a few spoonful’s on hamburger buns.