Preheat the oven to 400 degrees F. Spread the asparagus on a nonstick baking sheet in a single layer, then drizzle with the olive oil and season with salt and pepper. Roast for 15 to 20 minutes. When the asparagus is finished, remove it from the oven and immediately drizzle with the toasted sesame oil and seeds. (as a note, I like to whisk together the aioli and then poach the eggs while the asparagus is roasting.)
To assemble the toasts, drizzle the toast with a tablespoon or so of the lemon garlic aioli. Layer a few asparagus spears on top – as many as you want – followed by the egg. Season the egg with a bit of salt and pepper then sprinkle some green onions on top. Serve immediately.
lemon garlic aioli
Whisk together the dijon mustard, egg yolk, garlic and lemon juice in a large bowl until combined. Slowly stream in the olive oil while continuously whisking until the mixture emulsifies and comes together completely. Whisk in the whole grain mustard and taste, then season with salt and pepper as desired.