Bring a large pot of water to a gentle boil. Prepare an ice bath in a large bowl. Working in two batches, boil the asparagus until just tender, 5 to 7 minutes. (Be careful not to overcook the asparagus, as they will lose their shape and start to wilt.) Transfer the cooked asparagus to the ice bath to stop cooking and then drain on a paper-towel-lined plate.
In a small bowl, mash the egg yolks and mustard to a paste with a fork. Add the vinegar and whisk to combine. While whisking, add the oil in a slow, steady stream to make an emulsified sauce. Stir in the capers, cornichons, tarragon, 1/2 teaspoon salt and 1/4 teaspoon pepper. Taste and adjust the seasoning to your liking. Refrigerate until ready to use.
To plate, crisscross a few asparagus on six individual plates. Drizzle a bit of sauce all around and on top, and sprinkle with a few edible flowers if desired (they add color to the plate and are perfect for a springtime celebration).
I find it easiest to lay the asparagus on a board while peeling them so they don't snap. I also trim the bottoms of the asparagus so they are all the same length, as I find it presents better on the plate.