Add the oil to a Dutch oven or large heavy-bottomed pot set over medium-high heat; heat until shimmering. Add the celery, onion and carrot and cook, stirring occasionally, until the vegetables are softened and browned around the edges, 5 to 6 minutes. Reduce the heat to medium and stir in the tomato paste, chili powder, cumin, cayenne, garlic, 1 teaspoon salt and 1/2 teaspoon pepper. Cook until the garlic and spices become fragrant and the tomato paste begins to brown, about 2 minutes. Add the turkey, breaking it up with the back of a wooden spoon. Season with another 1 teaspoon salt and 1/2 teaspoon pepper. Return the heat to medium high and cook, stirring occasionally, until the turkey is cooked through and starting to brown, 6 to 7 minutes. Add the tomatoes, beans and stock and bring to a boil. Reduce to a simmer and cook until the chili is thickened, about 30 minutes. Add additional salt and pepper to taste.
Stir in the squash noodles and cook until tender, 5 to 7 minutes. Garnish with a dollop of sour cream and a sprinkle of scallions.
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