Mix the egg, milk, 3 tsp butter, cardamom, sugar and orange zest all in a bowl. Whisk until combined well. Slice the buns in half and flatten them slightly with a rolling pin.
Heat a frying pan and add the remaining butter. While that is melting, soak one slice of the bun into the egg mix and leave it for few seconds. Place the dipped bun into the pan and cook on low to medium heat for 1 minute on each side until nice and golden. Serve the buns warm with a scoop of ice cream.