Spread 4 bread slices with 1 tablespoon cream cheese each; spread the other 4 slices with 1 teaspoon marmalade each. Combine to make 4 sandwiches.
Whisk the whole eggs, egg whites, orange zest and juice, and vanilla in a shallow bowl. Place the bran flakes in a resealable plastic bag and crush with a rolling pin or your hands. Pour the crumbs onto a plate. Dip both sides of each sandwich in the egg mixture, then in the crumbs, gently pressing the crumbs onto the bread.
Heat 1 tablespoon each oil and butter in a skillet or griddle over medium heat. Add the sandwiches in batches and cook until the outsides are golden and the insides are melted, 3 to 4 minutes per side. (Add more oil and butter, if needed.)
Slice the French toast sandwiches into triangles. Let cool before serving to little ones, as the cream cheese can get quite hot. Sprinkle with confectioners' sugar, if desired, and the kids won't even ask for syrup!