Kale Soup With Potatoes and Sausage

linguiça or uncured Spanish chorizo, cut across into 1/8-inch-thick slices

large onion, peeled and chopped

garlic, peeled and minced

large baking potatoes, peeled and cut into 1/4-inch cubes

heads kale, stemmed and coarsely chopped (about 6 cups)

chicken broth, homemade or low-sodium canned

balsamic vinegar

kosher salt

Freshly ground pepper

plum tomatoes, cored and cut into 1/2-inch dice