In a large bowl, whisk the flour, sugar, baking powder, salt, and cinnamon together.
Add the butter and use a pastry cutter, two knives, or your fingers to work in the butter until it's the size of small peas.
Pour in the milk and stir until everything is combined.
Gently knead the dough until it comes together. It should be just sticky enough to hold together. Cover and refrigerate until you're ready to fry.
If cooking over a campfire, prepare a hot fire. Pour enough oil into a small Dutch oven or pot to reach a depth of 2 inches. Attach a deep-fry thermometer to the side of the pot.
Set it over the hot fire, or on a camp stove or stovetop over high, and heat to a temperature of 350°F.
Pinch off rounds of dough and shape them into golf ball-sized balls. Work with the dough just long enough to create a ball; don't overwork it or your doughnut will be tough.
Working with 3 or 4 at a time, add them to the oil and cook until golden brown all over, 3 to 3 ½ minutes. Check one after the first batch to determine the optimal cooking time for your dough. Use a slotted spoon or spider to carefully remove the doughnuts from the hot oil and transfer them to paper towels to drain.
Repeat with the remaining dough, letting your oil return to temperature between batches.