See cooking notes below.
Beat eggs, milk, salt and pepper in bowl until blended.
Heat 1 teaspoon butter in large nonstick skillet over medium heat until hot. Pour in egg mixture. As eggs begin to set, gently pull the eggs across the pan, forming large soft curds. Continue cooking, pulling, lifting and folding eggs until thickened and no visible liquid egg remains. Do not stir constantly. Remove from pan. Clean skillet.
Spread remaining 2 teaspoons butter evenly on one side of each bread slice. Place 2 slices in skillet, buttered side down. Top evenly with scrambled eggs, cheese and bacon. Cover with remaining bread, buttered side up.
Grill sandwiches over medium heat, turning once, until bread is toasted and cheese is melted, 2 to 4 minutes.
Avoid cast iron. Eggs scrambled in a cast iron skillet can turn a greenish shade. This harmless but unappealing color change is the result of a chemical reaction between iron in the pan and sulfur in egg whites.
Don't overcook. The heat retained in the pan will continue to cook and firm up the eggs after pan is removed from heat.
How long to beat is a matter of preference. Light beating produces more dense scrambled eggs. Vigorous beating aerates the eggs, resulting in lighter fluffier curds.