In a medium bowl. Whisk the flour, sugar, baking powder, salt, cinnamon and nutmeg until blended.

Add the milk and shortening, and stir until mixture forms a scraggly dough.

Scrape dough out onto a lightly floured counter, and knead a few times until it forms a smooth ball.

Roll dough out into ½-inch thickness. Lightly dip a doughnut cutter into flour, and press out circles (do not twist the cutter, press down and pull up quickly!). Reroll scraps and repeat cutting out doughnuts until there’s no more dough left. Separate doughnut holes from doughnuts.

Fill a 4-quart pot halfway with a mixture of half oil and half shortening. Heat over medium-high until hot and shimmering (375ºF). Meanwhile, set a wire rack over a rimmed baking sheet.

If you plan to coat doughnuts, whisk cinnamon and sugar in a small bowl or prepare glaze for dipping.

Add one doughnut hole to test oil. It should sizzle vigorously immediately (if it doesn’t oil isn’t hot enough).

Once oil is ready, add a few more doughnut holes, making sure not to overcrowd the pot (or else they’ll steam instead of fry). Cook until deep golden, 1–2 minutes, then flip and cook until deep golden on other side, 1 to 2 minutes more. Transfer to wire rack. Let doughnuts drain 1 to 2 minutes, then roll in cinnamon sugar or dip in glaze while still warm (return to wire rack and let glaze set).

Repeat with remaining doughnut holes and doughnuts (doughnuts will take an extra 1 to 2 minutes per side).