In a large mixing bowl, add flour, yeast, sugar, and salt. Whisk until well combined. Set aside.
In a small pot, add milk and butter. Place over low heat until it’s warmed through and the butter has melted, warm to the touch when you dip your finger in, not scalding hot, (65ºC/150ºF on a thermometer). Ensuring it doesn’t come to a simmer/boil. Turn off the heat once the butter has melted.
Add beaten egg to the dry flour mixture followed by the warm milk mixture, mixing it immediately with a wooden spoon to avoid the egg cooking from the warm milk. TIP: once you add the egg, slightly mix it through the flour then add the warm milk, this will ensure the egg from scrambling.
Mix until well combined and the dough has formed. Transfer dough to a lightly floured surface, kitchen counter, or large chopping board.
Knead the dough for 5 minutes until smooth and elastic, sprinkling a little flour at a time if needed to prevent it from sticking to the bench.
In a large mixing bowl, big enough so your dough can double in size, add 1/2 tsp of olive oil and spread it on the base and around the sides of the bowl with a paper towel or pastry brush.
Transfer your dough into the bowl and cover with a tea towel or cling film. Place in a warm place for 1 hour and 30 minutes until the dough has doubled in size.
Line a large flat baking tray with parchment paper and set aside.
Gently remove dough from the bowl and onto a lightly floured surface.
Take a rolling pin and gently roll the dough out to an 8-inch (20cm) circle, about 1/2 inch (2cm) in thickness.
Using a 2 1/2 inch (6cm) round cookie cutter, cut out circles from the dough. You should get 12 doughnuts, re-rolling excess dough to create more.
Carefully transfer dough rounds to the lined tray. TIP: use a flat spatula to transfer them from the bench to the tray so they remain circular. Leaving a 2-inch (5cm) space between each one to allow for rising, refer to the in-post images.
Cover the tray with a tea towel or cling film and sit in a warm place for 1 hour until puffed up and they have increased in size, not quite doubled in size. Whilst they’re rising, preheat the oven to 190ºC (375ºF).
Remove the towel/cling film and transfer to the oven to bake for 10-12 minutes, until golden all over.
Whilst they're baking, melt the butter and combine the cinnamon and sugar for the cinnamon sugar coating, ready to coat the doughnuts immediately after baking.