Preheat oven to 220C / 425F. Spread asparagus in a single layer on a lined baking sheet. Drizzle with olive oil, season generously, toss to coat. Roast 10-12 minutes. Scatter Parmesan in the last 2 minutes until golden.
Step 2 — Poach the eggs
Bring a wide saucepan to a gentle simmer. Add vinegar. Crack each egg into a ramekin, swirl the water, slide in. Cook 3-4 minutes for runny, 5 for set. Drain on a towel.
Note: Cafe trick — poach all eggs, hold in warm water, reheat 30 seconds before serving.
Step 3 — Assemble
Toast sourdough. Optional: rub with cut garlic while warm. Layer: toast, asparagus, egg. More Parmesan, lemon zest, olive oil drizzle, chilli flakes, fresh herbs. Eat immediately.