Using 2 forks, gently combine chicken, shallot, garlic, sage, carrot, mustard, salt, and pepper. Loosely shape mixture into 2-inch patties (about 1/2 inch thick), being careful to not overwork. Place sausage patties on a baking sheet.
Heat 1 tablespoon oil in a nonstick skillet over medium-high heat. Working in batches, cook sausage patties until cooked through and golden brown, 2 to 3 minutes per side. Add more oil to skillet between batches as needed. Serve warm with chutney.