Step 1

Mix vinegar and sugar in a small bowl. Add shallot and let sit until softened, 5–10 minutes; drain.

Step 2

Meanwhile, place radishes in another small bowl and pour in very cold water to cover (radishes should curl).

Step 3

Place eggs in a medium pot and pour in water to cover by 3". Add a large pinch of salt and bring to a boil over high heat. Immediately cover, remove from heat, and let sit 8 minutes.

Step 4

Run 1 egg under cold water; crack and peel. Yolk should be bright yellow and texture more chalky than fudgy. Let remaining eggs sit longer in water if needed, checking in 1-minute increments until done. Drain and rinse eggs under cold running water. Transfer to a large bowl of ice water and let sit, stirring every minute or so, until mostly cool, about 5 minutes. Carefully peel eggs, then trim a very small amount of white from top and bottom of each egg so they can stand on an end. Slice in half crosswise. Separate yolks from whites, transferring yolks to a small bowl. Place whites on a large plate.

Step 5

Mix mustard powder and 2 tsp. cold water in another small bowl to make a paste. Scrape into a food processor; add raw egg yolk, lime juice, and yuzu kosho; pulse until smooth. Let sit 1 minute.

Step 6

With motor running, pour in ½ cup oil, starting with a few drops at a time, then increasing to a very thin stream. Process until incorporated, then add 1 tsp. cold water. Stop processor and scrape down sides, then, with motor running, add remaining ½ cup oil in a very slow stream. Process until incorporated. Season mayonnaise with salt or up to 1 Tbsp. more yuzu kosho. Add cooked yolks to mayonnaise and pulse, scraping down sides as needed, until a very thick paste forms. Add shallot, cornichon, and 2 Tbsp. herbs to egg mixture and pulse to combine. Taste and season with more salt if needed.

Step 7

Transfer egg mixture to a pastry bag fitted with pastry tip of choice, or a resealable plastic bag (snip one corner off to pipe), and chill.

Step 8

When you’re ready to serve, arrange egg whites cut side down on paper towels and let drain. Turn over and pipe in a generous amount of filling. Drain radishes, pat dry, and place a slice on top of each egg, then sprinkle with more finely chopped herbs.Do ahead: Eggs can be cooked and mayonnaise can be made 1 day ahead. Cover and chill separately.