3/4 lb mushrooms, finely chopped
1/4 cup finely chopped shallot
2 tablespoons unsalted butter
1/2 teaspoon salt
1/4 teaspoon black pepper
2 tablespoons crème fraiche or sour cream
1 tablespoon finely chopped fresh tarragon
12 slices Black Forest or Virginia Ham (without holes; 10oz)
12 large eggs
Garnish: fresh tarragon leaves
Accompaniment: buttered brioche or challah toast
Special equipment: a muffin tin with 12 (1/2 cup) muffin cups
Preheat oven to 400 degrees F.
Cook mushrooms and shallot in butter with salt and pepper in a large, heavy skillet over moderately high heat, stirring, until mushrooms are tender and liquid they give off is evaporated, about 10 minutes. Remove from heat and stir in crème fraiche and tarragon.
Assemble and Bake:
Fit 1 slice of ham into 12 lightly oiled muffin cups (ends will stick up and hang over edges of cups). Divide mushrooms among cups and crack 1 egg into each. Bake in middle of oven until whites are cooked but yokes are still runny, about 15 minutes. Season eggs with salt and pepper and remove (with ham) from muffin cups carefully, using 2 spoons or small spatulas.
* The eggs in this recipe are not fully cooked, which may be of concern if salmonella is a problem in your area.