
Preheat oven to 425 degrees F. Lightly oil a baking sheet or coat with nonstick spray.
To make the tarragon vinaigrette, whisk together olive oil, vinegar, shallot, mustard and sugar in a small bowl; stir in tarragon and season with salt and pepper, to taste. Set aside.
Place asparagus onto the prepared baking sheet. Stir in olive oil and garlic; season with salt and pepper, to taste.
Place into oven and roast for 12-15 minutes, or until tender but crisp.
Serve immediately, topped with eggs and Parmesan, drizzled with tarragon vinaigrette.