Step 1

Whisk both flours, baking powder, baking soda, salt, and nutmeg in a medium bowl. Using an electric mixer, beat butter and both sugars on high speed until light and creamy, 2-3 minutes. Add eggs one at a time, beating to blend and scraping down bowl between additions. Beat in vanilla.

Step 2

Reduce speed to low. Gradually add dry ingredients; mix just to combine. Fold in oats and raisins.

Step 3

Divide dough between 2 large sheets of parchment paper. Using paper as an aid, roll up each piece of dough into a 1 1/2-inch diameter log. Wrap in plastic; freeze for at least 4 hours and up to 3 weeks.

Step 4

Preheat oven to 350°. Unwrap dough and cut into 1/2-inch-thick rounds (return unused dough to freezer); place 2-inch apart on a parchment paper-lined baking sheet.

Step 5

Bake cookies until edges are golden brown, 15-18 minutes. Transfer to a wire rack; let cool. DO AHEAD: Cookies can be baked 2 days ahead. Store airtight at room temperature.