Add the flour, baking powder, baking soda, sugar, salt, nutmeg, and lemon zest to a medium bowl. Whisk to blend everything together.
Using a fork or whisk, beat the buttermilk and egg together in a small bowl. Pour over the flour mixture. Add the strawberries. Stir together just until it forms a thick batter (a spoon should be able to stand freely in the batter). Let it rest for 5 minutes.
Add 1 1/2-inches (4-cm) of oil to an 8-inch skillet. Heat until shimmering.
Meanwhile, add some sugar and cinnamon (as much or little as you like) to a small bowl, and stir to mix, if you’d like to coat the doughnuts. Also, set up a wire rack over a rimmed baking sheet.
Once the oil is ready, drop 1 1/2 tablespoonfuls of batter into the oil. You should be able to fit 6 in the pan. Cook until deeply golden underneath, and the batter looks cooked halfway through. Using a fork, flip the doughnuts. Continue cooking until golden all around. Transfer the doughnuts to the wire rack. Let drain for 15 seconds, then roll in the cinnamon sugar, if you like. Let cool a few more minutes before trying to eat. Repeat with the remaining batter.
Doughnuts are best eaten within 2 hours.