Whisk together egg whites and water in a shallow bowl.
Spread bread crumbs on a plate.
Dip cheese rounds in egg, letting excess drip off, then dredge in bread crumbs, pressing lightly so they adhere, and put on a plate.
Refrigerate for 15 minutes.
Heat olive oil in a 12” nonstick skillet over moderately high heat until hot but not smoking.
Add cheese rounds and cook, turning once, until golden, about 1 minute total.
Remove from oil and drain on a paper towel lined plat. Remove skillet from heat.
Toss salad greens of choice in a light dressing (i.e. Washington Dinner Train Dressing) and arrange on plates.
Top with warm goat cheese croutons.