In a medium bowl, whisk together mayonnaise, capers, mustard, dill, and lemon zest.
Add eggs to mayonnaise mixture and coarsely mash with a potato masher. Season to taste with salt and pepper.
Spread about half of egg salad on bottom halves of buns. Layer with radishes and lettuce, then add remaining egg salad, dividing equally. Top with remaining bun halves.
Wine pairing: A bright, citrusy white like Cliff Lede 2014 Sauvignon Blanc (Napa Valley; $25) makes a zingy match with the capers. --Sara Schneider