Pasta Salad with Tomatoes, Mozzarella, and Chickpeas

Using the side of a chef's knife, mash garlic with 1 teaspoon salt into a paste. Transfer to a small bowl; whisk in lemon juice, vinegar, oregano, and oil. Stir in 1/4 teaspoon each salt and pepper. In a fine-mesh sieve, toss tomatoes with 1 teaspoon salt; let stand 15 minutes to drain.

Cook pasta in generously salted water according to package directions until cooked all the way through. Drain (but don't rinse, which would waterlog the noodles), then spread on a rimmed baking sheet and toss with half of vinaigrette. Let cool completely, about 20 minutes.

Meanwhile, in a large bowl, toss fennel, capers and brine, chickpeas, mozzarella, and salted tomatoes with remaining vinaigrette. Add pasta; toss to combine. Season with salt and pepper. Refrigerate up to a day ahead; let stand at room temperature at least 30 minutes before serving. (Cold pasta salad is too firm and less flavorful.) Toss with Parmigiano-Reggiano and parsley; serve.