Slice the Montrachet into 12 (1/2-inch-thick) slices. (The easiest way to slice goat cheese is to use a length of dental floss.) Dip each slice into the beaten egg whites, then the bread crumbs, being sure the cheese is thoroughly coated. Place the slices on a rack and chill them for at least 15 minutes.

For the dressing, place the vinegars, sugar, salt, pepper, and egg yolk in the bowl of a food processor fitted with a steel blade and blend for 1 minute. With the motor running, slowly pour the olive oil through the feed tube until the vinaigrette is thickened. Season, to taste.

Toss the salad greens with enough dressing to moisten, then divide them among 6 plates.

Melt 1 tablespoon oil and 1 tablespoon butter in a saute pan over medium-high heat until just under smoking. Cook the goat cheese rounds quickly on both sides until browned on the outside but not melted inside. Top each salad with 2 warm rounds and serve.