In a mixing bowl, beat the eggs. Add the milk, yogurt, and vanilla, and stir until incorporated. Pour the mixture evenly between two 9×13-inch pans.
Place the bread in the yogurt mixture, flipping and making sure that both sides are thoroughly coated. Cover the pans with plastic wrap, and refrigerate overnight. Carefully, turn the slices once or twice during this time to make sure they absorb plenty of the custardy yogurt mixture.
The next morning, prepare a hot nonstick griddle or frying pan with oil or butter. (If you prefer the flavor of butter, mixing in a little oil will help prevent the butter from burning.)
Lightly brown each side of the bread, cooking slowly over low heat. I start the bread on medium heat to get a nice golden brown color and then reduce the heat and wait patiently. This will ensure the insides are thoroughly and evenly cooked and the outsides are a little crispy.
Top the cooked bread with additional yogurt, fresh fruit, and/or maple syrup.