Whisk the egg yolk, pressed garlic, and anchovy paste together until combined. Whisk in Worcestershire sauce and Dijon mustard.
Slowly whisk in the olive oil, just a drop at at time, until the dressing thickens and the olive oil is completely mixed in. Stir in the Parmesan cheese, red wine vinegar, and lemon juice. Taste and season with salt and pepper.
Keep the dressing covered in the refrigerator until ready to use, and ideally for at least an hour (to let the flavors blend together).
For the Roasted Asparagus:
Preheat the oven to 425 F.
Trim any rough stems off of the asparagus. Line a rimmed baking sheet with parchment paper, and spread the asparagus onto it. Drizzle the asparagus with avocado oil, then sprinkle with salt and pepper.
Toss the asparagus to evenly coat the spears with oil, salt, and pepper. Roast the asparagus at 425 F for 8-12 minutes, or until tender on the outside but still slightly crunchy inside.
For the Toasted Breadcrumbs:
Pour one teaspoon of olive oil into a small pan over medium-low heat. Once the oil is warm, sprinkle in the breadcrumbs and Italian seasoning. Stir the breadcrumbs into the oil to coat them, then cook for a few minutes until they turn golden brown. Stir often so the breadcrumbs brown evenly. Transfer them to a plate lined with paper towel.
To Build the Asparagus Caesar Salad:
Transfer the roasted asparagus to a small serving platter. Drizzle with Caesar dressing, then top with toasted breadcrumbs, more finely shredded Parmesan, and freshly cracked black pepper. Serve hot!