Brown sausage over medium heat in a Dutch oven or large, heavy-bottomed pot, breaking it apart into small bits with the edge of a stiff spatula. Remove the sausage to a paper towel-lined plate, leaving 1 teaspoon of fat in the pot.
Add the chard to the pot, and toss to coat with remaining fat. Cook for 5 minutes, until chard is well wilted.
Pour in olive oil. Grate the garlic onto the chard, sprinkle with salt and pepper, and toss several times to distribute the garlic, and coat the leaves evenly. Cook for 2-3 minutes more, until chard is wilted, and garlic is fragrant. Remove chard to the plate with the sausage.
Add beans and broth to the pot, and bring to a simmer over medium heat. Mash beans slightly with a potato masher.
When soup is heated, stir in sausage and chard, and serve.