Slice the jam-filled doughnuts in half (optional for better soaking).
In a bowl, whisk together eggs, milk, sugar, vanilla extract, and cinnamon.
Heat butter in a non-stick pan over medium heat.
Dip each doughnut piece into the egg mixture, coating well but not soaking too long.
Place on the pan and cook until golden brown on both sides.
Flip carefully to avoid breaking and cook evenly.
Remove from pan and serve warm.
Optionally dust with powdered sugar or add extra jam for serving.