Freeze the cheese about 10 minutes, then cut off the rind and slice the cheese into 1-inch cubes. (Freezing makes it easier to cut.) Whisk the eggs, milk, parsley and chives in a bowl; season with salt and pepper. Heat a large nonstick skillet over medium-high heat, then add the butter. When the foam subsides, add the egg mixture and cook, undisturbed, until the edges set, about 30 seconds. Using a rubber spatula, pull the set egg around the edges into the center of the pan. Repeat, drawing the spatula around the edge of the pan, until most of the eggs are set, about 5 minutes. Scatter the cheese on top and let melt slightly, then fold the eggs over the cheese. Remove from the heat and let sit until the cheese melts, about 1 more minute.