1 small bulb Fennel
2 medium Leeks, white and light green parts only, halved lengthwise and rinsed carefully to remove any dirt from inner layers
16 medium Cremini or White Mushrooms, (about 1 pound)
2 Shallot
1 tablespoon plus 1 teaspoon Olive Oil
1 14-ounce package Puff Pastry, (like Dufour), defrosted according to package directions
3 Eggs
8 ounces Goat Cheese
Salt and Pepper
Heat oven to 400 degrees. Trim fennel of green top and root end, reserving fronds, and quarter bulb from top to bottom. Using a mandoline or very sharp knife, cut fennel, shallots and leeks into paper-thin slices. Clean and slice mushrooms.
Heat 1 tablespoon oil in a skillet over medium heat; add fennel and leeks and sauté until just tender but not brown, about 6 minutes. Transfer to a bowl and set aside. Heat remaining teaspoon of oil in skillet over medium-high heat; add mushrooms and sauté until they release all their liquid and most of it boils away, about 5 minutes. Combine fennel mixture with mushrooms and sauté together briefly; season with salt and pepper. Remove pan from heat.
Unfold puff pastry onto lightly floured surface; cut in half lengthwise to form two long rectangles. Gently roll out each rectangle to approximately 5 by 14 inches and place on cookie sheet (or cut into two circles, if desired). Trim edges by 1/4 inch strips all around; set strips aside. Break one egg into a small bowl; beat slightly. Brush edges of pastry with some egg. Use trimmed strips to make a raised border on each. (Or, fold pastry edges over to form a rim.) Brush entire surface with remaining beaten egg. Prick interior of pastry all over with a fork. Bake until pale gold, about 10 minutes. If pastry has puffed up inside edge, press it down gently. Set aside.
Meanwhile, combine remaining eggs with 6 ounces goat cheese and blend until smooth. Spread onto pastry. Return to oven and bake just until set, about 4 minutes. Remove from oven and spread with mushroom-leek mixture. Crumble remaining cheese on top. Just before serving, broil tarts on low heat for 2 to 3 minutes, until tarts are warm and cheese softens. Garnish with fennel fronds.