Cut the 2 whole chicken breasts in half to make 4 pieces. Remove the skin and any bits of fat. Season lightly with salt and pepper on both sides, then place the breasts between 2 sheets of wax paper and flatten lightly and evenly with a meat pounder or heavy bottle.

In a large skillet, heat 3 tablespoons butter and saute the fennel or celery, leeks, and mushrooms over low heat for 1 minute, stirring, then add the broth, salt lightly, cover, and cook very gently about 5 minutes, or until almost tender; check to see if more broth is needed – the vegetables should not brown. Push the vegetables to the edges of the skillet and add the remaining 1 tablespoon butter.

Quickly dredge the chicken breasts in flour, shaking off the excess, and add them to the pan. Saute them gently 30 seconds on one side, then turn them, strew the vegetables on top, and add the champagne. After it has boiled up for a few seconds, stir in the cream, cover, reduce heat, and cook gently 5 minutes. The sauce will have thickened; if it is too thick, stir in a little more broth or Champagne. Taste and correct the seasoning if necessary.

Serve with rice.