Heat a large frying pan over a medium heat. Combine the sugar and cardamom powder in a bowl until evenly blended. Pour the mixture on to a flat plate and smooth it out.
Put the eggs, milk, orange zest and vanilla bean paste in a bowl and beat until evenly combined.
Pour into a shallow dish with a flat base and soak 2 slices of brioche in the mixture for about 45 seconds. Flip them over and soak for another 45 seconds.
Meanwhile, melt half the butter in the warm pan. Fry the 2 soaked slices of brioche for 2 minutes on each side until puffed up (which indicates that the egg is cooked) and golden brown. Immediately place the cooked brioche slices in the cardamom sugar, coating it well on both sides, then transfer to a plate.
Repeat with the remaining 2 slices of brioche and serve immediately.