In the bowl of a stand mixer, combine the egg, milk, sugar, salt, flour, and sourdough starter.
Mix on speed 1 for 5 minutes to obtain a smooth dough.
Knead on speed 2 for 10 to 15 minutes, until the dough pulls away from the sides of the bowl.
Add the diced butter and knead on speed 1 until fully incorporated and the dough pulls away from the sides of the bowl.
Let the dough rest for 1 to 1.5 hours at room temperature (20-25°C/68-77°F), until it has doubled in volume.
Deflate the dough and shape it into a ball.
Place the dough in the bowl, cover with plastic wrap, and refrigerate for 12 hours.
Remove the dough from the refrigerator and Let it rise for 5 to 7 hours.
Fold the dough to release the air and divide it into 70g portions.
Shape the portions using a cookie cutter.
Let the mannele rest at room temperature for 1.5 to 2 hours.
Brush the mannele with egg and bake them.