Choose arugula, basil, or mustard microgreens for a pretty and peppery finish.
Arrange eggs in a single layer in a large saucepan with enough salted water to cover. Bring to a boil; cook 1 minute. Cover pan; remove from heat. Let stand 8 minutes; drain.
Place eggs under cold running water until just cool enough to handle. Tap eggs on a hard surface until cracks form; peel. Discard shells.
Combine vinegar, oil, 1/4 teaspoon salt, 1/8 teaspoon pepper, and radishes in a small bowl; toss to coat. Set aside.
Slice eggs in half lengthwise; carefully remove yolks. Combine egg yolks, butter, mayonnaise, and mustard in the bowl of a food processor; process until smooth and light, scraping bowl as needed. Stir in remaining 1/4 teaspoon salt and remaining 1/8 teaspoon pepper. Spoon or pipe yolk mixture evenly into egg white halves (about 1 tablespoon per egg half). Top filled eggs evenly with radish mixture. Arrange egg halves on a serving plate; sprinkle evenly with microgreens.