Cover eggs with an inch of water in a saucepan. Bring to a boil, cover, remove from heat and let stand 12 minutes. Transfer to ice water for 10–15 minutes, then peel.

Halve eggs lengthwise. Mash yolks with mayonnaise, mustard, vinegar and salt until smooth. Pipe or spoon into the whites.

Set a tomato half, cut-side down, onto each filling mound as a hat. Pipe a narrow sour-cream band around its base. Chill until serving.