Cook pasta according to package directions, adding asparagus to the water for the last 2 minutes of cooking; drain. Rinse with cold water; drain again. Transfer pasta mixture to a large serving bowl.
Add green onions, mint, and cheese to pasta mixture. Using a serrated knife, remove peel and white pith from two of the oranges. Halve oranges lengthwise, then slice crosswise. Add orange pieces to pasta mixture.
For dressing, finely shred enough peel from the remaining orange to measure 2 teaspoons. Squeeze enough juice from the remaining orange to measure 2 tablespoons. In a screw-top jar combine orange peel, orange juice, oil, vinegar, salt, and pepper. Cover and shake well.
Drizzle dressing over pasta mixture; toss gently to coat. Cover and chill for 1 to 24 hours. Toss again before serving.
