Heat the vegetable oil in a large skillet over medium-high heat. Add the chorizo, scallions, garlic and orange, red and yellow peppers and cook, stirring occasionally, until the chorizo is browned and has turned the oil red, 6 to 8 minutes.
Add the tomato paste, Cajun seasoning, salt and pepper, then stir and cook for 1 minute more. Stir in the chicken broth, heavy cream and Worcestershire sauce. Next, add the gnocchi and bring to a simmer. Simmer the mixture until the gnocchi has softened and cooked, 3 to 5 minutes. Stir in the Parmesan and sprinkle with basil leaves to serve.
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