Line two large baking sheets with parchment paper or silicone baking mats. Set aside.
In the bowl of a stand mixer or a large bowl, cream together 1/2 cup (1 stick) of unsalted butter and 3/4 cup packed brown sugar. Mix on a medium-high speed for 1-2 minutes with a paddle attachment until the mixture becomes lighter in color.
Add in 1 large egg and 1 tsp of vanilla extract and mix on a medium-high speed until the mixture is smooth.
Then mix in 3/4 cup all-purpose flour, 1/2 tsp baking soda, 1/2 tsp ground cinnamon, 1/2 tsp salt, and a pinch of ground nutmeg on a low speed just until incorporated.
Stir in 1 1/2 cups of rolled oats and 1 cup of butterscotch chips with a rubber spatula. The dough should be quite thick and sticky at this point!
Scoop or roll out 15 equal-sized cookie dough balls (about 3 Tbsp of dough each) and place them on one of the prepared sheets. You can wet your hands lightly with water to make it easier to roll out the cookie dough if you do this by hand. Be prepared, your hands will get sticky and covered in dough!!
Place the cookie sheet in the fridge for 30 minutes. As the cookies chill, preheat the oven to 350°F/175°C.
Rearrange the cookie dough balls between the two prepared baking sheets, spacing them 3 inches from one another.
Bake for 13-14 minutes. The centers of the cookies will look a bit soft and underdone, but they will firm up as the cookies cool.
Let the cookies cool on the pan for 10 minutes, then place them on a wire rack to finish cooling and enjoy!