Preheat the oven to 400 degrees . Line 2 baking sheets with parchment. Working with 1 puff pastry sheet at a time, cut the pastry crosswise into quarters, then halve lengthwise to form 8 rectangular pieces. Cut each piece diagonally to form 16 triangles. Repeat with the remaining puff pastry sheet.
Working with 1 puff pastry triangle at a time (and refrigerating the remaining pastry as needed), 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, olive oil, 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.
