Asparagus: To cook the asparagus, bring a medium pot of water to a boil. Meanwhile, fill a medium bowl with ice and water and set it aside. Salt the boiling water generously, and add the asparagus. Cook until tender-crisp, about 1-2 minutes, then using a slotted spoon, transfer the asparagus to the prepared ice bath. Let cool for 2 minutes, then drain and pat the asparagus dry. Add more ice to the ice bath
Beets: To roast beets, position a rack in the middle of the oven and preheat to 400 degrees. Scrub the beets, and trim off any leaves and roots. Wrap each beet in a large piece of aluminum foil. Place the wrapped beets on a rimmed baking sheet and roast for 30-50 minutes depending on the size and thickness of the beets, or until a knife slides easily into the beet. Let the beets sit until they are cool enough to handle, then discard the foil and peel the skins. Cut into chunks for the salad.
Hard-boiled eggs: Gently lower the eggs into the boiling water. Adjust the heat so that the water maintains a simmer. After 8 minutes, use a slotted spoon to transfer the eggs to the prepared ice bath. Let sit for about 5 minutes, then remove the eggs, crack and peel them, and halve them lengthwise. Yolks will be slightly soft in the center and a brilliant yellow-orange in color.
Chicken: To poach boneless, skinless chicken breasts, cut the chicken in half or thirds crosswise, depending on how large the pieces are. In a medium saucepan over medium heat, combine 3 to 4 cups of water, the chicken and 1 tsp. of salt. Stir once or twice and slowly bring to barely a simmer- do not let the water come to a boil. Reduce the heat to medium-low and gently cook until an instant-read thermometer reads 165 degrees when inserted into the thickest pieces of chicken, 10-15 minutes. Remove the chicken and let cool completely before dicing.
Make the vinaigrette: In a small bowl whisk together the olive oil, vinegar, and mustard until combined and stir in the scallions. Season to taste with salt and pepper.
In a large, shallow serving bowl or platter, scatter the lettuce leaves. Arrange neat rows of the asparagus in the center of the platter, then arrange a row of chicken cubes (if you are using). Pile the chunks of beets along the bottom of the platter, then arrange a row of cucumber slices along the sides and maybe avocado at the top rimmed with thin slices of radish. Tuck the halved eggs here and there and sprinkle the halves of garden fresh cherry tomatoes over all and add cheese (optional). Serve with the vinaigrette on the side or drizzled over the salad.