Heat the oil in a large saucepan over medium heat. Add leeks and cook 6 minutes, stirring frequently, or until softened. Add garlic and cook 1 minute. Stir in rice and cook 1 more minute. Stir in broth, 1/2 cup at a time. Stir frequently until liquid is absorbed before adding the next 1/2 cup (about 20 minutes total); rice should be tender yet firm to the bite.