For chimichurri, process herbs, garlic, onion and jalapeño in a small food processor until blended, then add oil and process until smooth. Add vinegar, season generously to taste and process to combine.
Heat a char-grill or barbecue to medium-high. Drizzle chorizo with olive oil and grill, turning occasionally, until browned and cooked through (3-4 minutes). Drizzle asparagus and bread with olive oil and grill, turning occasionally, until asparagus is just cooked and bread is toasted (1-2 minutes). Rub bread with cut side of garlic, then tear into pieces. Combine chorizo, asparagus, bread, piquillo peppers and onion in a bowl, drizzle with a little chimichurri and toss to combine. Arrange on serving plates, scatter with rocket and oregano and serve drizzled with extra chimichurri.