Preheat oven to 400 degrees F.
Heat 2 Tbsp olive oil to medium-high in large, heavy bottom pot. Add the sausages and cook until golden brown on all sides, and fully cooked inside.
Wipe the sausages with a paper towel to make sure they are dry. Brush egg wash on both sides of the pastry, and place sausage on top. Pinch the puff pastry closed together around the sausage and gently roll the dough to secure it. Cut into 4 equal pieces and place seam side down onto the baking sheet. Brush with egg wash. Using a knife, cut a few slits in the dough.
Transfer to oven and bake for 15-18 minutes.
Meanwhile, for the chimichurri, in a food processor pulse all ingredients together until well combined. Be careful not to over-pulse as you want the sauce to have texture. Add more olive oil, if needed. Season well with salt and pepper, to taste.
Remove sausages from oven and serve immediately with chimichurri.