Preheat oven to 350°F (175°C), rack in the middle.
Line 2 or 3 baking sheets with parchment paper. If you don't have any parchment paper, spray lightly with non-stick spray.
Mix the flour, baking soda, cinnamon, salt, and nutmeg together in a bowl. Set aside.
In the bowl of your mixer cream the butter with the paddle on low or medium-low until smooth. Takes a minute or two.
Add the brown and white sugar a bit at a time on medium until all is added and incorporated and the butter is kinda fluffy. 2-3 minutes.
On medium speed add the egg and vanilla.
On low speed add the flour mixture a heaping tablespoon at a time until all added and combined.
Add the oats and mix on low speed.
Add the raisins (or cherries) and finish mixing.
Remove bowl from mixer and using a spatula or a wooden spoon mix a bit more to pick up any stray oats and/or raisins and/or cherries.
Form 1-tablespoon balls and arrange on a sheet pan -- should be able to get 12-15 on a pan.
Bake one pan at a time, 11-14 minutes, turning halfway through. (In my oven it's 6 minutes, turn, then 7 minutes.
Remove pan from oven and set whole pan on a cooling rack or range-top. Let cookies cool and set on the pan for 5-10 minutes before removing to a cooling rack to cool completely. They'll be a bit soft still right out of the oven and may "droop" if you try to move them too quickly.