Mixed-Bean Soup with Andouille and Celery

extra-virgin olive oil

leeks, white and pale-green parts only, halved lengthwise, thinly sliced, and washed well (about 4 1/2 cups)

red-pepper flakes

Coarse salt and freshly ground pepper

andouille or other smoked sausage, cut on the bias into 1/4-inch-thick slices

sprigs thyme

chicken broth

(about 15 ounces each) beans, such as cannellini, roman, and black-eyed peas, drained and rinsed

stalks celery, thinly sliced (about 1 cup), plus celery leaves, for garnish