Activate the yeast

• In a large bowl, combine the lukewarm milk, yeast and sugar.
• Stir well and let stand until foamy.

Make the dough

• Add the egg, butter, flour and salt.
• Knead until smooth and elastic.

Let the dough rise

• Cover the dough and let it rise until doubled in size.

Shape the donuts

• Deflate the dough and divide it into 12 equal pieces.
• Shape each piece into a ball, then roll into a long rope of even thickness.
• Hold both ends and twist them in opposite directions, bring the ends together so the dough twists around itself, then pinch firmly to seal.

Second rise

• Place the donuts on parchment paper and let them rise until doubled in size and noticeably puffy.

Fry the donuts

• Heat the oil in a deep skillet over medium-high heat to 170 °C.
• Fry the donuts in small batches until golden brown, turning once.
• Drain on paper towels.

Make the brown butter glaze

• In a small saucepan over medium-high heat, melt the butter for the glaze.
• Cook until it turns light brown and gives off a nutty scent, then remove from the heat and let cool until lukewarm.
• Whisk together the brown butter, powdered sugar and milk until smooth and slightly thick.

Glaze and serve

• Let the donuts cool for a few minutes.
• Dip the top of each donut into the glaze and let any excess drip off.
• Allow the glaze to set briefly before serving.