Preheat a water bath to 181 degrees. In a medium bowl, season one-third of the radishes with salt and white pepper. Transfer them to a 1-gallon vacuum-pack bag, arranging them in a single layer, and vacuum-seal. Submerge the bag in the water bath and cook at 181 degrees for 20 minutes. Fill a bowl with ice water. Transfer the bag to the ice bath; let cool.

Meanwhile, in a bowl, combine the lemon zest and juice with the orange zest and juice, shallot, sugar, and vinegar. Whisk in 1 cup of oil; season with salt and white pepper.

In a grill pan, heat a thin layer of oil. Add one-third of the radishes and cook over moderately high heat, turning, until browned and just tender, 7 minutes; transfer to plates with the sous vide radishes and remaining fresh radishes, drizzle with the vinaigrette, sprinkle with salt, and serve.