Heat oven to 400 degrees. Heat 1 tbsp 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, 1/2 cup of water, and 1/4 tsp each of salt and pepper; bring to a boil. Nestle the sausages in the beans.
Sprinkle remaining olive oil over the sausage mixture. Transfer skillet to the oven and bake for 25 to 30 minutes.