Whisk the eggs and milk in a large bowl to combine. Fold in the corn, bread crumbs, cheese,  parsley, baking powder, 1 teaspoon of salt, and ½ teaspoon pepper. Transfer the mixture to a food processor and pulse until there are no longer any whole corn kernels, 30 to 45 seconds (see chef’s note below). Return the mixture to the bowl, cover with plastic wrap and refrigerate for 1 hour.

Heat the oil in a large skillet over medium-high heat. Working in batches, scoop ¼ cup of the batter at a time with a large serving spoon and carefully slide the batter into the skillet to form oval latkes approximately ¼-inch-thick. Fry until golden brown on both sides, flipping once, about 2 minutes per side. Transfer to a paper towel-lined tray and repeat with the remaining latkes, adding more oil to the skillet as needed. Serve immediately, hot from the pan with tzatziki and radishes — or eat the leftovers as a snack at room temperature.