Carrot Chickpea Burgers

Name: Carrot-Chickpea Burgers
Ingredients: ¼ cup extra-virgin olive oil, plus more for drizzling; 1 tablespoon finely chopped garlic (from 3 cloves); 1 cup grated carrots (from 2), plus more for serving; Kosher salt (we use Diamond Crystal) and freshly ground pepper; 1 can (15.5 ounces) chickpeas, drained; ½ cup cooked white rice; ½ cup panko breadcrumbs; 1 large egg; ¾ cup packed chopped fresh cilantro, plus leaves for serving; ½ cup full-fat Greek-style yogurt; Little Gem lettuce, for serving