Crack the eggs into a medium sized bowl. Tip: crack eggs on a flat surface to minimize shell fragments. Add water or cream to the eggs and whisk to combine, until eggs are a uniform color throughout.
Preheat a medium sized non-stick or cast iron skillet over medium-low heat. Add butter and once it melts and foams, add the egg mixture.
Cook for 2 minutes or so, until the eggs' edges begin to set. Using a silicone spatula, slide the eggs from the edge of the skillet toward the center. Continue working this way along the edge of the skillet until the runny egg no longer moves back toward the edges of the pan. When cooked, the eggs should look like large curds. Sprinkle with salt and pepper. Remove from heat.
To assemble
Lay out the bread slices, 4 will be the bottoms, and 4 will be the tops of the sandwiches. Place a slice of cheese on each of the bottom slices. Cover each cheese slice with 1/4 of the scrambled eggs and then another slice of cheese. Cover them with the top slices. Spread the softened butter on the outside of the bread.
Heat a griddle or large skillet over medium-high heat. Add the sandwiches to the pan buttered side down, leaving some space between each (don't overcrowd the pan).
Cook for 3 minutes or until bread is golden brown. Use a large spatula to flip sandwiches over and cook for 3 more minutes, or until the cheese melts.