Put the warm milk into a large bowl and sprinkle over the yeast and a pinch of sugar; let stand for a few minutes, until it gets foamy. Add the remaining sugar, half the flour, and the butter, egg and salt and stir until well combined and sticky. Add the remaining flour and stir until the dough comes together, then knead - by hand or with the dough hook attachment on your stand mixer - for about 5 minutes, or until it’s smooth and elastic. It should be tacky, but not overly sticky.
Shape the dough into a ball, place in a greased bowl and cover with a tea towel for an hour or two, until doubled in size. Take out the dough and roll or pat it out on a lightly floured surface to about 3/4 inch thick. Cut into doughnuts using a doughnut cutter, or use a cookie cutter or glass rim, then cut a smaller hole in the middle or poke and stretch one out with your finger. (Cut them as close together as you can to avoid having to reroll the scraps - I just cook the scraps as is, rather than try to make more doughnuts.) Cover the lot with a tea towel and let sit for 1/2-1 hour to puff up again. (They'll get puffier still as they cook.)
When you’re ready to fry your doughnuts, heat about 1 1/2 inches of oil in a wide, heavy pot set over medium-high heat until it’s hot, but not smoking - if you have a candy thermometer it should be about 350?F, or you could take a scrap of the dough and dip it in - if it sizzles and bubbles around the dough, it's ready to go.
Gently lower a few doughnuts at a time into the oil - you don't want to crowd the pot, or it will cool down the oil and the doughnuts could get oily and heavy - and cook for a minute, until golden on the bottom. Gently flip (tongs or a bamboo skewer work well for this) and cook until golden on the other side. Remove with a slotted spoon and transfer to a paper towel-lined plate or baking sheet to cool.
Set a wire rack over a sheet and place the doughnuts on it, and place your cereals in shallow dishes. Whisk together the glaze ingredients and dip the doughnuts, then dip in the cereal. Place on the rack and add extra cereal to fill in any gaps, if needed.
Makes about 1 1/2 dozen doughnuts.