1 (10 ounce) package cream cheese, softened
1/4 cup melted butter
36 eggs
1 (3 ounce) package instant French onion soup mix
1 cup milk
3 cups shredded Swiss cheese, divided
Beat cream cheese, butter, eggs, soup mix and milk into a medium bowl. Stir until well blended. Chill 1 hour or overnight.
Preheat oven to 375 degrees F (190 degrees C).
Dredge ham, cheese and of the remaining 1/2 cup Swiss cheese in egg mixture. Place mushrooms and peppers on top of this mixture. Spread mushroom mixture into a 3-inch disc shape shape. Top with cream cheese mixture, then top with ham mixture. Repeat layering few times. Place half of Swiss cheese on top of mushroom mixture. Cover and refrigerate overnight.
After 2 to 3 hours, slice slices from mushroom mixture, and roll into 1-inch balls; pinch edges to seal. Place on serving platter. Cover and refrigerate overnight to allow cheese to soak.
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