Heat oven to 400º F. Heat 1 tablespoon of the oil in a large ovenproof skillet over medium-high heat.
Add the sausage and cook, turning, until browned and cooked through, 5 to 6 minutes. Transfer to a plate.
Add the carrots and garlic to the skillet and cook for 1 minute. Add the chard and cook until wilted, 1 to 2 minutes.
Add the beans, ½ cup water, and ¼ teaspoon each salt and pepper; bring to a boil. Nestle the sausages in the beans.
In a bowl, combine the bread crumbs and the remaining teaspoon of oil. Sprinkle over the sausage mixture. Transfer the skillet to oven; bake until golden, about 25 minutes.