1. Preheat oven to 425°. Cut puff pastry sheets in half lengthwise. Cut 1/4-inch-wide strips off every side of each piece, resulting in 8 long strips and 8 short. Brush a 1/4-inch-wide border on the 4 larger bases with egg wash, and place cut pastry strips on top to form a raised edge. Press gently to adhere. Chill pastry.
2. Mix goat cheese with half the herbs in a small bowl until soft and creamy. Spread evenly in the bottom of each tart, and chill.
3. Heat olive oil in a skillet, and add leek and green onions. Sauté until tender and translucent, about 5 minutes. Cool to room temperature.
4. Place leek mixture on goat cheese down the center of each tart. Sprinkle with remaining herbs, and place on a baking sheet. Brush pastry edges with remaining egg wash, and bake 18 to 20 minutes or until pastry is golden brown and puffs. Slice and serve warm or at room temperature.