Wash the cherry tomatoes and slice each tomato in half; peel and trim the garlic clove.
Bring a large pot of generously salted water to a rolling boil.
Add the drained chickpeas to the boiling water briefly until the water returns to a full boil, then remove the chickpeas with a slotted spoon and set aside.
Return the water to a boil and cook the orecchiette until al dente following the package instructions, reserving at least 1 cup of the pasta cooking water before draining.
In a food processor, combine half of the reserved chickpeas (about 8 oz), the basil leaves, one ladle of pasta water, and 2 tablespoons of olive oil; puree until smooth and season with salt to taste.
Heat 2 tablespoons of olive oil in a large skillet over medium-high heat and add the whole garlic clove; when fragrant, add the halved tomatoes and sauté very briefly (about 30–60 seconds) so they warm but stay firm.
Add the drained orecchiette, the pureed chickpea mixture, and the reserved whole chickpeas to the skillet with the tomatoes; toss and cook together for about 1 minute, adding pasta cooking water as needed to loosen the sauce.
Remove from the heat, adjust seasoning with salt if needed, and serve immediately.
