Combine water, lemon zest, and cinnamon stick in a pot and bring to a boil.

In a large bowl, mix together flour, baking powder, sugar, and salt.

Add butter to the boiling water and stir until melted.

Remove cinnamon sticks and lemon zest from the water.

Pour the boiling water mixture into the dry ingredients, mixing quickly to form a dough.

Incorporate one egg at a time until fully blended into the dough.

Heat oil in a deep fryer or large pot to 350°F (175°C).

Drop spoonfuls of dough into the hot oil and cook until golden brown and puffed up evenly.

Do not pierce the doughnuts with a fork while frying.

Remove doughnuts from the oil and drain on paper towels.

Transfer the doughnuts to another dish lined with paper towels to cool further.

Once cooled, roll the doughnuts in a sugar and cinnamon mixture.