Step 1Slice both ends off each orange, cutting just deeply enough to expose the juicy flesh. Setting the fruit on end, use a paring knife to carve away the skin and pith in a series of smooth, arcing strokes from top to bottom, rotating the orange a little with each stroke as you work your way around the sphere; then go back and trim any pith you may have missed. Then cut into half-inch pinwheel slices. Place a layer of slices on each of 4 plates.
Step 2Trim the bottoms of the asparagus to the point where they aren't bitter. (Start by trimming off a half inch or so, then cut a little slice and taste; trim a little more as needed, until it doesn't taste bitter.) Peel the asparagus spears, all the way to the flower. Place a spear flat on a cutting board, then drag a vegetable peeler back and forth on the surface to shave beautiful ribbons of asparagus. Continue shaving until it's difficult to go on. Drop the ribbons from that spear onto the oranges on one plate; continue with the rest, using one spear per plate.
Step 3Peel back the roe sac from the compressed bottarga, and use the fine holes of a grater (Microplane works best) to shave 1 teaspoon over the oranges and asparagus on each plate.
Step 4Drizzle 1 1/2 teaspoons olive oil over each salad.