In a small saucepan melt 1 tablespoon of the butter over medium heat. Add the shallot; cook and stir about 2 minutes or until softened.
Stir in the tarragon, kosher salt, and pepper. Whisk in the mustard, vinegar, and lemon juice. Cook for a minute and remove from heat. Whisk in the mayonnaise. Heat through, stirring frequently. Cover and keep warm.
In a medium skillet heat the remaining 1 tablespoon butter over medium-high heat. Add the prosciutto pieces and cook about 2 to 4 minutes or until just crisp and golden, turning once halfway through cooking time. Transfer to paper towels to drain.
Bring a large saucepan of salted water to a boil. Add asparagus and cook about 3 minutes or until crisp-tender; drain.
Assembly
Transfer asparagus to a serving platter. Spoon the tarragon sauce over asparagus spears and sprinkle with prosciutto and chopped eggs.