1 tbsp. olive oil
5 tbsp. butter
1 small yellow onion, peeled and thinly sliced
4 oz. cep, chanterelles, morels, or other wild
mushrooms, cleaned and thinly sliced
Salt and freshly ground black pepper
2 tbsp. crème fraîche
Leaves from 1 sprig fresh tarragon, chopped
1. Heat oil and 2 tbsp. of the butter together in a large non-stick skillet over medium-high heat. Add onions and cook, stirring often, until soft, 3–5 minutes. Add mushrooms and cook, stirring often, until soft, 3–5 minutes. Season to taste with salt and pepper, then transfer to a small bowl and set aside. Wipe skillet clean with paper towels and set aside.
2. Crack eggs into a medium bowl and thoroughly beat with a fork. Add crème fraîche and tarragon, season to taste with salt and pepper, and mix well.
3. Return skillet to medium-high heat. Melt the remaining 3 tbsp. butter in the skillet. Pour eggs into skillet and keeping it away from heat, turn it around so that the egg mixture spreads around like a pancake. Return to heat. When eggs are starting to set (in about 30 seconds), spoon mushroom filling down center of eggs. Carefully fold sides of omelette over filling and cook for 1 minute more. Slide omelette onto a warm serving platter with shavings of parmesan and fresh tarragon leaves.