Clean mushrooms with a small soft brush or paper towel. Brush off excess pine needles and dirt, and tear the mushrooms into smaller pieces.
Heat olive oil and shallots in a small sautê pan over medium heat and season with the salt. Add mushrooms and cook for 4-5 minutes (or until the mushrooms are fully cooked but not overly soft). Remove from heat and set aside.
Preheat oven to 325°F. In a bowl, beat eggs well and mix in mushrooms, 3/4 cup of cheese. Salt and pepper to taste.
Heat olive oil in a small skillet or omelet pan over medium-low heat and pour in egg mixture. As soon as the bottom is solidified and lightly browned, sprinkle 1/4 cup of the Ossau-Iraty over the top and place pan into preheated oven. Bake for fifteen to twenty minutes (or until the top of the frittata has set), remove and cool five minutes before inverting and serving.