Preheat oven to 350F. Grease the muffin pan with olive oil.
Dice the ham, slice the green onions.
Wash the mushrooms and place on a kitchen paper to dry.
In a deep bowl, beat the eggs. Add the heavy cream and spices along with ham cubes and sliced green onions.
Adjust salt, pepper and spices to taste.
Fill each cavity of muffin pan with the egg mixture.
Bake in oven for 4-5 minutes.
Remove from the oven and add the mushrooms on the top.
Bake for 8 more minutes or until the eggs are mostly set.
Add Cheddar cheese and cook for one more minute.