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Preheat oven to 375°F. In large pot of boiling water, cook pasta, stirring occasionally, until al dente, about 9 minutes. Drain pasta and rinse with cold water.
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Meanwhile, in a large nonstick skillet, heat oil over medium-high and swirl to coat pan. Add onion, bell peppers, and garlic and cook, stirring often, until softened, about 8 minutes. Stir in chickpeas and oregano and cook, stirring often, until heated through, about 2 minutes. Remove chickpea filling from heat and stir in cheese, 1 teaspoon of vinegar, ¼ teaspoon of salt, and ¼ teaspoon of black pepper.
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In medium bowl, whisk tomato sauce, sugar, paprika, and the remaining 2 teaspoons of vinegar, ½ tsp teaspoon of salt and ½ teaspoon of black pepper.
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Lightly coat 2-quart baking dish with nonstick spray. Spread tomato sauce in bottom of dish. Stuff chickpea filling, about 3 tablespoons each, into pasta shells.
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Arrange stuffed shells in baking dish. Spoon any remaining filling over tops of shells. Bake shells until filling is heated through, 20 to 25 minutes.