Cupcakes: In medium bowl stir together flour, baking powder, baking soda, salt, cinnamon, ginger and nutmeg. In large bowl cream together butter and sugar until light and fluffy; beat in eggs. Blend in pumpkin. Stir in dry ingredients and milk, blending until batter is smooth. Stir in chopped walnuts. Spoon batter into paper lined muffin tins. Fill about 2/3 full. Bake at 375°F/190C for 18 to 22 minutes.
Frosting: In 2 quart/2 liter saucepan melt butter over medium heat. Add brown sugar and half-and-half. Continue cooking, stirring occasionally, until mixture comes to a boil (2 to 3 minutes). Remove from heat and add powdered sugar and vanilla; beat until well mixed (1 to 2 minutes). Let cool to spreading consistency (5 to 10 minutes). Frost cupcakes.
Makes 16 cupcakes.