Heat oil in a large nonstick skillet over medium-high heat. Add shallots and garlic; cook 1 minute, stirring occasionally. Add mushrooms, leek, 1/4 teaspoon salt, thyme, and 1/8 teaspoon pepper; cook 4 minutes or until mushrooms are tender. Add Madeira; cook 1 minute or until liquid evaporates. Transfer mushroom mixture to a bowl; cool 5 minutes. Stir in cheeses and parsley.
Slice each breast half lengthwise, cutting to, but not through, other side. Open halves, laying breast flat. Place each breast half between 2 sheets of heavy-duty plastic wrap; pound to 1/4-inch thickness using a meat mallet or small heavy skillet. Sprinkle chicken with remaining 1/4 teaspoon salt and remaining 1/8 teaspoon pepper.
Divide mushroom mixture into 4 portions; spoon each portion down center of each breast half; leave a 1/2-inch border at each end. Fold sides over filling.
Place a 2-foot-long sheet of heavy-duty plastic wrap on a work surface with 1 long side hanging over the counter's edge 2 inches. Place a stuffed breast half, seam side down, on the end farthest from you; tightly roll the breast toward you, jelly-roll fashion. Twist the ends in opposite directions to form a cylinder. Tie plastic wrap in tight knots against the breast half on each end. Trim off excess wrap close to the knot. Place a second 2-foot-long sheet of heavy-duty plastic wrap on the work surface; place rolled breast on wrap, and repeat procedure. Repeat with remaining breast halves.
Bring 3 quarts water to a boil in a large stockpot; add chicken. Simmer 15 minutes (do not boil), turning occasionally. Remove from water, and let stand 10 minutes before unwrapping and cutting into 1/2-inch-thick slices.