Preheat the oven to 375 degrees F. Generously butter four 6-ounce ramekins and dust with cornmeal; tap out the excess.
Whisk the milk, corn, cornmeal and a pinch of salt in a large microwave-safe bowl and microwave 5 minutes. Stir and continue to microwave until thick, about 2 more minutes. Meanwhile, beat the eggs in a bowl with a mixer until thick and airy, about 5 minutes.
Whisk 1/2 cup cheese and 1 tablespoon chives into the hot cornmeal mixture until thick. Whisk half of the cornmeal mixture into the eggs, then whisk in the remaining cornmeal mixture until smooth. Divide the batter among the prepared ramekins and sprinkle with the remaining 1/4 cup cheese. Transfer the ramekins to a baking sheet and bake until puffed and set, 20 to 25 minutes.
Meanwhile, chop the tomatoes and toss with the olive oil, the remaining 1 tablespoon chives, and salt and pepper. Top the spoonbread with the tomato mixture. Serve with pickled vegetables.