In the bowl of a stand mixer fitted with a dough hook, add the milk, eggs, flour, sugar, yeast, salt, and butter. Knead on medium speed until smooth and elastic. The dough should pass the windowpane test.
Lightly spray a baking dish with cooking spray – my favourite is a 23×30cm Pyrex glass dish. Transfer the dough to the dish, turning it to coat the surface. Flatten it to fill the dish evenly, and cover with clingfilm.
Leave to rise in a warm place until nearly doubled in size, approximately 1 hour.
In the meantime, prepare 2 baking trays lined with parchment paper; spray lightly with cooking spray.
Lightly flour your work surface. Pat the dough into a slightly larger rectangle – around 2cm thick – and dust with a little flour.
Using a long knife, cut the dough into 24 pieces. Place them onto the prepared trays, loosely cover with clingfilm or clean kitchen towels, and leave to rise again for around 30 minutes.
While the beignets are rising, heat a generous amount of neutral oil in a deep-fryer or a heavy-bottomed pot to 180°C.
Put the icing sugar into a brown paper bag or a large bowl.
Fry 4–6 beignets at a time, turning with a metal spider or tongs, until deep golden brown, around 1-1½ minutes per side.
Transfer the hot beignets straight into the bag of icing sugar, close tightly, and shake well to coat. Place on a cooling rack over a tray. Repeat with the remaining beignets, adding more icing sugar as needed.