Drain beans, reserving 2 tablespoons liquid. Transfer to a bowl and mash. Stir in shallot, carrot, cornmeal, and sage. Season with salt and pepper. Add 1 tablespoon reserved liquid. If mixture is too dry, add the other.
Heat a large skillet over medium-high heat. Add 2 tablespoons oil. Form mixture into 12 patties (about 2 1/2 inches diameter each) and saute in batches until golden brown and crisp, 2 to 3 minutes per side. Repeat with remaining oil and patties. Season patties with salt and serve with Roasted Tomato Sauce.