Place the egg in a shallow dish, and the breadcrumbs in another shallow dish.
Dip the cheese round in the egg, and then coat all sides with the bread crumbs, pressing to adhere. Set aside.
Heat 2 tablespoons of the butter in a small skillet over medium heat just until it starts to brown. Brown cheese on all sides. Remove to a serving plate and keep warm.
Wipe out the skillet with a paper towel and add the remaining 2 tablespoons butter to the skillet. Melt over medium heat and when foamy, sauté the onions for 2 minutes. Sprinkle sautéed onions over the cheese round and serve immediately with crackers.
Note: Don’t let the butter get too hot as you can easily burn the breadcrumbs.