Preheat oven to 375 degrees. In a large bowl, beat butter and sugars until creamy. Add egg and vanilla; beat well.
In another bowl, combine flour, baking soda, cinnamon, salt, and nutmeg; mix well. Gradually add to butter/sugar mixture, scraping down sides of bowl as needed. Add oats; mix well.
Drop by rounded tablespoons (I love using my cookie scoop) onto a Silpat or parchment lined cookie sheet. Bake 8-9 minutes for chewy cookies, or if you like your cookies more on the crisp side, 10-11 minutes. Store tightly covered.