Preheat oven to 425°F. Line rimmed baking sheet with parchment paper. Roll puffed pastry out on lightly floured surface and cut each sheet into 6 squares. Transfer squares to prepared baking sheet for easy assembly. Place 1-2 cheese slices on squares.
Toss asparagus with oil and season with salt and pepper. Divide asparagus evenly among squares, placing diagonally from one corner to another, ensuring all tips are facing same direction. Spoon 2-3 tablespoons of red pepper relish over each square. Fold two opposite corners of puff pastry squares over filling and press to seal. Brush puff pastry with beaten egg.
Bake bundles 12-15 minutes, until pastry is golden-brown and cooked through. Sprinkle each bundle with crushed red pepper and transfer to serving platter