Step 1

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 mayonnaise. Stir in 1/4 teaspoon each salt and pepper.

Step 2

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. Let cool completely, about 20 minutes.

Step 3

Meanwhile, in a large bowl, toss green beans, onions, capers and brine, and chickpeas with 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 basil; serve.