In a small bowl, combined the cheese, mayonnaise and garlic; spread over each muffin half. Placea baking sheet. Broil 4 to 6 inches from heat for 2 to 3 minutes or until golden brown. set aside

Place 2 to 3 inches water, and a large skillet with high sides; add vinegar, Bring to a boil; reduce heat and simmer gently. Break cold eggs, One at a time, into a custard cup or saucer; holding a cop close to the surface of the water, slip each egg into water. cook, Uncovered,until whites are completely set and yolks begin to thicken (but are not hard).,about 4 minutes.

Meanwhile,in a large skillet, sauté mushrooms and shallots in oil until tender. Stir in the cream,horseradish,mustard,white pepper and cayenne. Bring to a boil. Reduce heat; simmer 3-5 minutes or until slightly thickened m stirring constantly.

With a slotted spoon,lift each egg out of water. Top each muffin half with egg and 2 tbsp. Sauce. Sprinkle with chives. Serve immediately.