Preheat the oven to 400°F. Line 2 baking sheets with parchment paper.
Roll out pastry sheet a little and cut into 24 triangles.
Working with 1 puff pastry triangle at a time (refrigerate the rest of the pastry until ready to use), arrange a piece of sausage across the base of the triangle and roll up snugly, sealing the pastry with a dab of beaten egg. Transfer to the prepared pans. Brush the triangles with more beaten egg and bake until puffed and golden, about 30 minutes.
Meanwhile, using a food processor, blend the parsley, cilantro, garlic, EVOO, vinegar, crushed red pepper and 2 tablespoons warm water until almost smooth. Season with salt and black pepper. Serve the pigs in blankets warm, with the chimichurri dip.