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Spritz the baking pan with cooking spray.
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Combine the chicken, ham, nutmeg, half-and-half, and ground black pepper in a large bowl. Stir to mix well.
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Pour half of the mixture into the baking pan, then top the mixture with 3 slices of Swiss cheese, then pour in the remaining mixture and top with remaining cheese slices.
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Slide the baking pan into Rack Position 1, select Convection Bake, set temperature to 350ºF (180ºC) and set time to 15 minutes.
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When cooking is complete, the egg should be set and the cheese should be melted.
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Serve immediately.