Step 1

Preheat the oven to 350 degrees F (175 degrees C).

Step 2

Cream butter and brown sugar for cookies together in a bowl with an electric mixer. Stir in pumpkin, then egg. Add baking soda, baking powder, vanilla extract, salt, cinnamon, and nutmeg. Stir in flour. Mix in walnuts and raisins.

Step 3

Drop spoonfuls of dough 2 inches apart onto ungreased cookie sheets.

Step 4

Bake each sheet on the bottom rack in the preheated oven for 6 to 7 minutes; continue to bake on the top rack until edges are golden, 6 to 7 minutes more. Continue with remaining cookie sheets in this manner. Let cookies cool on the cookie sheets for 5 minutes, then transfer to a cooling rack to cool completely.

Step 5

While the cookies cool, melt brown sugar, milk, and butter for frosting in a medium pot over low heat. Bring to a boil; continue to boil mixture for 2 minutes, stirring constantly. Remove from heat and cool for 3 to 10 minutes. The longer the mixture is cooled, the thicker the frosting will be on the cookies.

Step 6

Add powdered sugar and vanilla extract to the frosting mixture, stir well, and drizzle or spread onto cooled cookies. Allow the cookies to cool for 1 to 2 hours before stacking.