In a medium-sized bowl, prepare the egg mixture by whisking together the eggs, milk, sugar, vanilla extract, ground cinnamon, and salt until combined well. If your bread is not already sliced, cut into even slices of desired thickness.
Preheat a griddle or large non-stick skillet over medium heat. Once heated, add a little of the butter and spread it evenly to coat the surface.
Dip each slice of bread into the egg mixture, making sure both sides are coated evenly. Allow the bread to soak for a few seconds on each side, but don't let it become soggy.
Place the soaked bread slices on the preheated griddle or skillet. Cook each side for 2 to 3 minutes or until golden brown and cooked through. Repeat with the remaining slices of bread, adding more butter to the griddle or skillet as needed. Adjust the heat if necessary to prevent burning.
If making multiple batches, you can keep the cooked French toast warm in a low preheated oven or covered on warm plate. Once all the French toast slices are cooked, transfer them to individual plates or a serving platter. Serve immediately with your favorite toppings, such as maple syrup, powdered sugar, fresh berries, or even whipped cream.