How to Make It
Preheat the oven to 350°. In a medium bowl, beat the eggs with the chopped tarragon. In a large, nonstick ovenproof skillet, heat 2 tablespoons of the olive oil until shimmering. Add the chanterelle mushrooms, season with salt and pepper and cook them over moderately high heat, stirring occasionally, until the mushrooms are browned, about 8 minutes.
Add the remaining 2 tablespoons of olive oil to the skillet. Add the beaten eggs and cook until they begin to set at the edges, about 30 seconds. Using a spatula, lift the edge and tilt the pan, allowing the uncooked eggs to seep underneath. Cook until the bottom is set, about 3 minutes. Sprinkle the cheese on top and bake the frittata for about 8 minutes, until fluffy and set. Slide the frittata onto a platter, cut into wedges and serve.
Cremini or oyster mushrooms can be substituted.