Chimichurri: In a bowl, mix parsley, garlic, oregano, chili, vinegar, salt, and pepper. Slowly whisk in the olive oil. Let stand for 30 minutes for the flavors to meld.
Salsa Criolla: In a separate bowl, mix onion, bell pepper, tomatoes, vinegar, oil, salt, and pepper. Also let stand.
Preheat the grill to medium heat. Prick the Chorizo with a needle or skewer. You can also carefully prick it several times with a fork to release excess fat (but gently, to avoid all the juice squirting out).
Grill the whole sausages slowly for about 20–25 minutes, turning them until they are almost fully cooked (internal temperature should be approximately 80 °C).
Remove the cooked Chorizo, slice it lengthwise (not completely through, so it stays together), and open it up like a butterfly.
Place the sausages back on the grill, cut-side down, and grill for another 5 minutes until a crispy, charred crust forms.
Slice the rolls or baguettes lengthwise (not completely through). Brush the inside of the bread with the fat that dripped from the Chorizo on the grill.
Briefly toast the bread on the grill (cut-side down) for 1–2 minutes until lightly crunchy.
Place one cut, grilled Chorizo into each bread roll. Generously top with Chimichurri and/or Salsa Criolla.
Serve immediately, hot.