Cut the sourdough bread into 10 to 12 thick slices. I like to keep them about ¾ inch to 1 inch thick.
In a shallow bowl or baking dish, whisk together the eggs, whole milk, brown sugar, vanilla extract, cinnamon, and salt until smooth.
Heat a large skillet or griddle over medium heat and add a little butter.
Dip each slice of bread into the egg mixture, turning to coat both sides. Let the bread soak briefly, but not so long that it becomes too soft.
Place the slices in the hot skillet and cook for 2 to 4 minutes per side, or until golden brown and cooked through. Repeat with the remaining bread, adding more butter to the skillet as needed.
Serve warm with maple syrup, butter, fresh fruit, or your favorite toppings.