Preheat oven to 350 F. Lightly oil a 12-cup muffin pan.
In a large heavy frying pan over medium-high heat, saute mushrooms and shallot in butter with salt and pepper, stirring, approximately 10 minutes or until mushrooms are tender and liquid they give off is evaporated. Remove from heat and stir in cre fraiche or sour cream and tarragon.
To Assemble, fit one (1) slice of ham into each prepared muffin cups (ends will stick up and hang over edges of cups). Divide mushrooms among the cups and crack one (1) egg into each.
Bake in middle of oven approximately 12 to 14 minutes, depending on number of servings being baked. Check the eggs after about 10 minutes baking time. When done, the whites should be completely set and the yolks beginning to thicken but not hard. Remove from oven.
Season eggs with additional salt and pepper. Remove eggs (with ham) from muffin cups carefully, using 2 spoons or small spatulas, and place on individual serving plates. Garnish with tarragon leaves and triangles of buttered toast leaned on the cups to dip in the yolk as desired.
Serve two eggs per person.
Makes 6 servings.
Baked Eggs and Mushrooms in Ham Crisps Recipe: https://whatscookingamerica.net/Eggs/BakedEggHam.htm