In a large pot of boiling salted water, cook the orecchiette until al dente. Drain, reserving 1/4 cup of the cooking water.
Meanwhile, in a medium, deep skillet, heat 1/4 inch of vegetable oil until shimmering. Add the chickpeas and cook over high heat until crisp, 4 minutes. Transfer them to a paper towel–lined plate, sprinkle with the cumin and coriander and season with salt and black pepper. Discard the oil and wipe out the skillet.
Add the olive oil, garlic and crushed red pepper to the skillet. Cook over moderately high heat until fragrant, 30 seconds. Add the tomatoes and cook until softened, 3 minutes. Add the chard and cook, stirring, until wilted, 5 minutes. Season with salt and black pepper.
Add the pasta and reserved cooking water to the skillet and cook over moderate heat, stirring until incorporated. Add the mozzarella and basil and toss. Spoon the pasta into bowls, sprinkle with the chickpeas and serve.