Step 1Whisk the all-purpose flour, cornstarch, sugar, baking powder, salt and baking soda together in a large bowl. In another bowl, whisk together the milk, butter, vanilla and 2 eggs. Add the milk mixture to the flour mixture and stir until ingredients are just incorporated and form a thick batter (lumps are OK). Stir in 1 cup cheese and the chives, and let the batter rest for 5 minutes.
Step 2While the batter rests, heat a 12-inch ovenproof nonstick skillet over medium-low heat for 5 minutes. At the same time, arrange a rack 4 inches from the broiler heat source, and heat the broiler to high. Pour all the batter into the skillet, and quickly smooth the top. Cook until bubbles break on the surface of the pancake, and the underside is golden brown, about 6 minutes. (If after 4 minutes you notice the underside of the pancake is already dark golden brown, reduce heat accordingly.)
Step 3Quickly crack each of the remaining 6 eggs evenly into the batter (crack them into a small bowl first if you’re worried about shell fragments getting in the pancake), arranging them so there will be 1 egg in the center of each of 6 wedges when you cut the pancake. If you’re daring enough, drop them from about 8 inches above the pancake so that when they hit the batter, they sink with enough force to keep them in a neat round (if not, crack them in and they will settle on their own while cooking). Season each egg with a pinch of salt and pepper, then sprinkle the remaining 1 cup cheese evenly over the top.
Step 4Place the skillet under the broiler and cook until the top is golden brown and the pancake is completely cooked through in the middle and the egg whites are set but the yolks are soft and jammy, 4 to 6 minutes. Transfer the pancake to a rack and let cool for 5 minutes. Cut the pancake into 6 wedges, sprinkle with more chives, and serve with syrup, if you like.