01 - In a mixing bowl, combine the chopped parsley, chives, tarragon, minced garlic, lemon juice, and Dijon mustard. Slowly drizzle in the olive oil while whisking continuously until the sauce is well emulsified. Season with salt and pepper to taste, then set aside at room temperature to allow the flavors to meld.
02 - Carefully separate the egg yolks from the whites, keeping each yolk intact. Place the yolks on a parchment-lined plate and transfer to the freezer for 30 minutes until they are firm to the touch but not completely frozen solid.
03 - In a shallow bowl or plate, combine the fine breadcrumbs with the grated Parmesan cheese, mixing evenly to distribute the cheese throughout.
04 - While the yolks are chilling, toss the trimmed asparagus spears with 1 tablespoon of olive oil, seasoning generously with salt and pepper. Heat a grill pan or heavy skillet over medium-high heat. Cook the asparagus for 5 to 7 minutes, turning occasionally, until tender-crisp with light charring. Remove from heat and keep warm.
05 - Remove the firm yolks from the freezer. Gently and delicately roll each yolk in the breadcrumb mixture, applying a light, even coating all around. Handle with care to avoid breaking the delicate yolks.
06 - Heat vegetable oil in a small heavy-bottomed saucepan to 340°F. Using a slotted spoon, carefully lower each coated yolk into the hot oil. Fry for 30 to 60 seconds until the exterior is crisp and deeply golden. Transfer to a plate lined with paper towels to drain briefly.
07 - Arrange the grilled asparagus spears on serving plates. Place the golden crispy egg yolks on top of the asparagus. Drizzle the herb sauce generously over and around the dish. Serve immediately while the yolks are still warm and crisp.