Bring a pan of salted water to the boil, then reduce to a simmer. Heat a griddle pan over a high heat and toast the bread. Move each slice to a plate or board and drizzle with a little oil. Snap the woody end off the asparagus, then griddle for a few minutes on each side, sprinkle with the paprika and divide between the pieces of toast. While the asparagus is grilling, poach the eggs in the simmering water for 3 minutes. Using a slotted spoon, remove the eggs and drain, then place them on top of the asparagus. Grate over the parmesan, then pick and sprinkle over the mint leaves.