Heat milk in a microwave-safe bowl until warm, about 30 seconds. Mix in 1/4 cup butter, 2 tablespoons plus 2 teaspoons honey, and salt until combined. Cool until lukewarm, 3 to 5 minutes.

Combine warm water and yeast in a small bowl. Let stand until dissolved and creamy, about 5 minutes.

Combine milk mixture and yeast mixture in the bowl of a stand mixer fitted with a paddle attachment. Add 1/2 of the beaten egg. Beat in flour, 1/2 cup at a time, until dough pulls together. Switch to the dough hook attachment and knead lightly until dough is wet and sticky but forms into a ball, about 5 minutes.

Grease a large bowl with 1 teaspoon softened butter. Use greased or wet hands to transfer dough into the bowl, turn to coat with butter. Cover with a damp cloth and let rise in a warm place until doubled in volume, about 1 hour.

Dust a work surface with potato starch. Deflate dough and turn it out onto the work surface. Divide dough into 4 equal pieces and form into rounds. Place a piece of parchment paper over one of the rounds and roll into a rectangle about 1/8-inch thick with a rolling pin; cut into 4 wedges. Brush each wedge with a little softened butter. Repeat with remaining dough rounds.

Roll each wedge up from the base towards the point. Brush a little bit of remaining beaten egg on the seam to seal. Bend each roll into a crescent shape.

Line baking sheets with parchment paper. Arrange crescents, seal-side down, onto the prepared baking sheets. Brush tops with remaining beaten egg.

Transfer crescents on the baking sheets to the cold oven. Preheat the oven to 365 degrees F (185 degrees C).

Bake in the preheated oven until golden brown, about 25 minutes.