Bring a medium pot of water to a boil. While the water is coming to a boil, fill a medium bowl with ice water and keep it nearby. Gently lower the eggs into the boiling water, set the timer for 8 minutes, then allow to the water to a boil and adjust the heat so that the water is at a simmer. When 8 minutes are up, remove with a slotted spoon and transfer to the ice bath. Let sit for about 4 minutes, then remove the eggs, crack and peel them, and cut them in half lengthwise.
While the eggs are cooling, rinse the same pot, fill it water and bring to a boil. Salt the water generously, and return to a boil. While the water is coming to a boil, fill a medium bowl with ice water and keep it nearby. Add the sugar snap peas and asparagus to the boiling water and cook for 2 minutes, then drain and immediately plunge the drained vegetables into the cold water to stop the cooking. Let them sit in the cold water for 2 minutes, then drain again.
Make the Dressing: in a small bowl combine the olive oil, vinegar, scallions, mustard, salt and pepper. If you prefer a smoother dressing this can be done in a mini food processor.
Scatter the lettuce into a large shallow serving bowl. Over the lettuce, make nice neat rows of the chicken, onions, asparagus, beets, goat cheese, sugar snap peas, and avocado. Tuck the halved eggs into the salad randomly. Drizzle the Scallion Vinaigrette over the salad, or serve it on the side.
Notes
Use chickpeas for a vegetarian version. Skip the cheese and eggs for a vegan version. And if you prefer your eggs more firmly cooked all the way through (I love a slightly jammy yolk) then up the cooking time from 8 to 10 minutes, before plunging the cooked eggs into an ice bath.