Preheat the oven to 375 degrees F (190 degrees C).

In a mixing bowl, beat butter, brown sugar, white sugar, egg, and vanilla extract until well combined. Beat in flour, baking soda, salt, cinnamon, nutmeg, and rolled oats until thoroughly mixed. Stir in butterscotch chips and coconut. Drop dough by tablespoonfuls about 2 inches apart onto the baking sheets.

Bake cookies in the preheated oven until bottoms are light brown, 7 to 8 minutes. If you prefer crunchier cookies, bake 9 to 10 minutes.