Preheat oven to 400 degrees. Line a large baking sheet with parchment paper.
Snap any thick woody root ends off of the asparagus shoots. Lay the asparagus in a single layer on the parchment paper and drizzle with the olive oil. Sprinkle with fresh rosemary leaves. Toss to coat.
On a cutting board, slice the blood orange in half. Take one of the halves and slice it very thinly, so thickly you can see through it. Place the orange slices around and underneath the asparagus. Take the remaining half of the orange and squeeze some of the juice over the asparagus, reserving some of the juice to squeeze over top just prior to serving. Season the entire pan generously with salt and pepper.
Roast for 15-20 minutes until asparagus is browned and crisp-tender, turning the asparagus halfway through cooking. Squeeze fresh blood orange juice over top just prior to serving. Serve hot.