To make the vinaigrette, combine the mustard, vinegar, and oil in a small jar with a lid. Secure the lid tightly, shake until well-combined, and set aside.
Preheat the oven to 400 degrees and line a baking sheet with foil. In a medium bowl, toss the asparagus with olive oil, salt and pepper, and lay on the prepared baking sheet in a single layer. Cook for 5-7 minutes, or until just cooked through. (If your asparagus is pretty thick, you may end up cooking 10-12 minutes...just check it after 7 and then cook an additional 2 minutes at a time, as needed, until done.)
Meanwhile, heat a skillet over medium heat and cook the bacon until slightly crisp. Remove to a paper towels and allow the grease to drain off. When the bacon is cool, rough chop into bite-sized pieces.
Drain the bacon grease and wipe the skillet clean. Drizzle a little olive oil or butter in the pan, over medium heat and add the eggs. Season with salt and pepper and cook the eggs to over-easy, making sure the yolks don’t break and are still runny, about 3 minutes (time will vary depending on your stove-top heat.)
To assemble, divide the romaine between two plates, top with half the bacon, tomatoes, asparagus spears, and avocado slices. Top each salad with 2 eggs, and drizzle the vinaigrette over the top. Serve immediately and enjoy!