Place potatoes in a heavy sauce pan and add enough water to cover them three-fourths of the way. Boil until tender but still firm, about 20 minutes. Drain. Place mayonnaise in a large heat-proof bowl. Whisk in vinegar, mustard, salt and pepper, then slice or chunk in the potatoes while they are still hot. Stir frequently while cooling. When salad is cool, add the dill. Refrigerate until chilled and toss with the broccoli right before serving.
to mix everything while the potatoes are hot. And to add a handful of lightly steamed broccoli florets from the garden right before serving. This tastes even better the second day.