Roll out pastry on floured surface to 13x10-inch rectangle. Cut off 1/2-inch-wide strip from all 4 sides. Brush edges with some of beaten egg, then press strips onto edges of pastry, pinching to form raised border. Brush border with egg; reserve remaining beaten egg. Transfer to baking sheet. Chill while preparing filling.
Steam asparagus just until crisp-tender, about 3 minutes. Transfer to bowl of ice water to cool. Drain. Cut off top 2 to 3 inches of asparagus tops; set aside. Coarsely puree remaining asparagus stalks in processor. Add remaining beaten egg, ricotta, 3 teaspoons oil, and salt; process until thick puree forms. Transfer to a bowl; sir in salami and 1/3 cup gruyere; season with pepper. Spread mixture evenly over pastry. Sprinkle with remaining 1/3 cup gruyere. Toss asparagus tips with remaining 1 teaspoon oil; arrange tips over filling.
Bake tart until filling is set, about 25 minutes. Serve warm or at room temperature. Serves 6 to 8 as appetizer or 4 main course servings.