Preheat oven to 325°F. Spread chickpeas in an even layer on a small rimmed baking sheet. Bake until chickpeas are dry on the outside but still creamy in the center, 30 to 35 minutes. Let cool 5 minutes.
Combine chickpeas, basil, oil, Parmesan, garlic, chile, salt, and pepper in a food processor. Process until mixture is creamy and chickpeas are finely chopped, about 30 seconds, stopping to scrape down sides of bowl as needed. Transfer mixture to a large heatproof bowl.
Bring a large pot of salted water to a boil over high. Add orecchiette (or the pasta of your choice) to boiling water. Cook, stirring occasionally, until al dente, 2 to 3 minutes for Homemade Orecchiette , or according to package directions. Using a slotted spoon, transfer orecchiette to pesto in bowl. Add ¼ cup pasta cooking liquid, and stir until a creamy sauce forms and coats orecchiette, about 30 seconds, adding additional cooking liquid, 2 tablespoons at a time, if needed to thin the sauce. Divide orecchiette evenly among 4 bowls, and sprinkle with additional Parmesan, if desired.
