Cook potatoes in boiling salted water, drain and cool slightly. Cut into ½ inch cubes.
Remove corned beef from the can; separate with a fork. Combine with potatoes, eggs, celery, and onion in a large bowl. Reserve. Blend dry mustard with lemon juice in a small bowl until smooth. Stir in sugar, salt, pepper and caraway seeds and add 1 cup mayo. Blend well and gently fold into potato mixture.
Spoon salad in a long strip on double thickness of foil; roll up, enclosing in foil. Press to form an even cylinder about 10 inches long. Fold in ends of foil to seal. Chill overnight.
To serve, carefully unroll potato salad onto a serving platter (it should be firm enough to hold its shape and slice easily.) Spread with ½ cup mayonnaise. Garnish with parsley, cherry tomatoes, and eggs and cut into even slices to serve.