Thinly slice the carrots. Melt half the butter in a frying pan with 2 tablespoons of vegetable oil. Cook the carrots and peas until softened, about 5 minutes, stirring occasionally. Stir 2 cups of water into the carrots and peas. Stir in the flageolet beans, salt and pepper. In an ovenproof casserole or Dutch oven cook the button onions in the remaining butter, the sugar, and 1/2 cup of water. Keep an eye on the onions. They should become syrupy. Stir the other vegetables into the onions. Arrange the vegetables on a serving platter and decorate with the mint leaves.
