Fill a small saucepan half full with water and stir in 1 tablespoon of white vinegar to help the eggs not to crack as they cook.  Cover and bring to a boil, then gently lower the 3 eggs into the boiling water with a spoon.  Lower the heat to a simmer and place the lid on askew.  Cook for 9 minutes, then immediately drain and place the eggs in an ice water bath to stop the cooking process and to speed up the cooling.  Once cool, peel the eggs and rinse off any shell fragments, then blot each egg dry with a paper towel.  Halve the eggs lengthwise and sprinkle with black pepper.

Tear off 8 pieces of Boston lettuce.  Rinse and blot dry with paper towel.  Arrange most of the leaves around the edge of the platter and put one or two in the middle to make a pretty base for the other salad ingredients.

Get all the salad ingredients ready.  Cut a quarter of a sweet onion, then slice it to get 12 curved slices.  Mellow the onion by soaking it in ice water, vinegar, milk or sprinkle it with salt.  Wait 15 minutes then rinse.  Blot dry the baby beets so the red juice doesn't bleed.  Cut a cucumber in half.  Score the outside of a cucumber with the tongs of a fork then thinly slice it.  Rinse and halve the grape tomatoes lengthwise.  Slice the Irish Dubliner cheddar cheese ⅛ inch thick.

Composing the salad is the fun part.  Arrange the salad ingredients in a way that looks pleasing to you on a large platter or on individual plates.  You might want to have two sections for most of the ingredients and one section for the cheese, sweet onion, and beets.

Whisk together the mayonnaise, vinegar, tarragon, and Dijon mustard in a medium bowl.  Sprinkle in the salt and black pepper, then add a pinch of sugar.  Gradually add the water to get it the right pouring consistency.  Whisk until smooth, then taste and adjust seasonings if necessary.

Just before serving, drizzle the homemade salad dressing on the salad.  Serve with Irish soda bread, boxty bread, or Irish brown bread.  Use it as a side dish with an Irish chip butty sandwich or with a steaming bowl of Dublin coddle or smoky cheese, potato, and ham soup.