Begin by preheating your oven to 350°F (175°C). This ensures that your baked scrambled eggs cook evenly and thoroughly.
In a large mixing bowl, crack open the 12 large eggs. Add 1 cup of milk, 1/4 cup of water, and 1 teaspoon of salt. Use a whisk to beat the mixture until it is well combined and slightly frothy. This will incorporate air into the eggs, which is essential for a light and fluffy texture.
Slowly add the 1/4 cup of melted and cooled butter into the egg mixture. Whisk gently to combine, ensuring that the butter is evenly distributed throughout the mixture.
Lightly grease your 9x13 inch baking dish with cooking spray or a bit of additional melted butter. Pour the egg mixture into the prepared dish, ensuring an even layer for consistent baking.
Place the baking dish in the preheated oven and bake for 25-30 minutes. Halfway through the baking time, use a spatula to gently stir the eggs. This will promote even cooking and prevent any overcooking around the edges.
The baked scrambled eggs are done when the center is set and a light golden color appears on the top. You can test this by inserting a knife into the center; it should come out clean.
Once cooked, remove the dish from the oven and let it cool for a few minutes before slicing into squares. Serve the baked scrambled eggs warm, garnished with fresh herbs or your favorite toppings, if desired.