Place the eggs in a large saucepan. Fill with enough cold water to cover the eggs by 1 to 2 inches. Bring to a full boil, remove from the heat and cover the pan. Wait 10-12 minutes before removing the eggs. Rinse with cold water and place them in a bowl of ice water to cool.
While the eggs are cooling, grill the corn. Rub the corn with olive oil and pinches of salt and pepper. Grill until lightly charred, about 5-7 minutes. Let the corn cool slightly before slicing the kernels off the cob.
When the eggs have cooled, peel the shells. Slice the eggs in half lengthwise and separate the whites and yolks. Push the yolks through a fine mesh sieve over a large bowl. Stir in the mayonnaise, Greek yogurt, mustard and 1 teaspoon salt until smooth. Use a pastry bag fitted with a round tip or a spoon to fill the egg whites with the yolk mixture.
Top each egg with grilled corn kernels, a cherry tomato slice, chives, a little caviar and a sprinkle of black pepper.