Bring 8 cups of water in saucepan to boil.
Add potatoes and cook uncovered until tender, about 12 minutes.
Test by piercing potatoes with a fork—if they pierce easily, they are ready. Drain potatoes and let cool.
In a small bowl, combine dill, olive oil, and vinegar; season with salt and pepper to taste. Whisk until well combined.
In a large serving bowl, combine potatoes with dressing and toss well.
Just before serving, add remaining ingredients through lettuce and toss to combine. Garnish with radish, if using.
