Fill a large pot of water 3/4 full and bring to a boil. Add the asparagus and cook until crisp-tender, 4 to 4 1/2 minutes. Using tongs, remove the asparagus from the boiling water and transfer to an ice bath to cool slightly. Once cool enough to handle, remove from the water and pat dry with a paper towel. Set aside until ready to use.
Heat a large saute pan and, when hot, add the bacon and render until crispy, 7 to 8 minutes. Remove the bacon from the pan with a slotted spoon and drain on a paper-lined plate. Reserve bacon and bacon drippings until ready to use.
In a medium bowl, combine the shallots, garlic, Dijon, honey and lemon juice. Whisk to blend. While continuing to whisk, add the olive oil to the shallot mixture in a slow, steady stream until completely combined and emulsified. Add the truffle oil, 1/2 teaspoon of the salt and 1/4 teaspoon of the pepper to the vinaigrette and whisk to combine. Place the arugula in a large bowl and drizzle with 1/2 cup of the vinaigrette. Season with 1/2 teaspoon of the salt, and toss to coat the lettuce evenly.
In a large, nonstick saute pan, heat the reserved bacon fat over medium heat, crack each egg individually and add to the pan. Cook eggs over easy.
To plate, place 3 spears of the asparagus onto each of 6 salad plates. Divide the salad among the 6 plates, top with 1 over easy egg, sprinkle the crispy bacon evenly around each plate and place strips of the Parmesan over the salad.