Melt the butter in a large stainless-steel skillet with a lid over medium heat. Add the brown sugar and whisk until it melts into the butter. Add the water and whisk until smooth. Cover and set aside while you prepare the French toast.
Whisk the whole eggs and egg yolks in a large bowel to blend. Gradually whisk in the milk, cream and vanilla. Dip the bread slices into the egg mixture, turning to coat and soak until they are completely moistened with the custard.
Recipe adapted from: Karamardian, Zov. Simply Zov: Rustic classics with a Mediterranean twist. Zov's Publishing, 2011.