In a skillet, stir the mushrooms, nutmeg, and white wine.
Over medium heat, bring the wine to a boil and simmer until the wine has reduced.
Stir the mushrooms until they begin to brown.
Remove the mushrooms from the skillet and let them cool.
In the same skillet, stir the onion sliced with the olive oil over medium heat until the onions turn golden brown.
Let the onions cool completely.
Place the cooled onions into the prepared pie shell.
Sprinkle the diced ham on top of the onions evenly.
Sprinkle 1 cup of the cheese on top of the ham.
Beat the eggs with the half and half.
Gently pour the egg mixture into the center of the filled pie shell.
Spoon the nutmeg mushrooms onto the top of the egg mixture in a single layer.
Sprinkle the remaining cheese on top of the mushrooms.
Bake at 350 degrees F. for 60 minutes or until the quiche is puffed, golden brown, and a table knife inserted in the center comes out clean.
Cool the quiche for at least 10 minutes.
Quiche may be refrigerated and reheated before serving.