Prepare the Batter: Whisk together the eggs, almond milk, white sugar, and vanilla in a bowl.
Soak the Bread: Working with one or two slices at a time, gently place the thick bread into the egg mixture. Allow each side to soak for about 20-30 seconds. The goal is for the bread to be thoroughly moistened but still hold its shape. Note: Thicker bread may need a slightly longer soak.
Cook: Carefully transfer the soaked bread to a preheated, buttered pan or griddle. Cook for approximately 3 to 4 minutes per side, or until the French toast is golden brown, cooked through, and has slightly crisp edges. Add more melted butter to the pan between batches as needed.
Serve: Remove the finished French toast from the pan and serve immediately. This dish pairs excellently with toppings such as maple syrup, powdered sugar, fresh berries, or whipped cream.