Heat oven to 350°F Combine brown sugar and 1/2 cup butter in large mixer bowl. Beat at medium speed, scraping bowl often, until creamy (1 to 2 minutes). Add egg and vanilla; continue beating until well mixed (1 to 2 minutes). Reduce speed to low. Beat, adding flour, baking powder and baking soda alternately with sour cream, until well mixed (1 to 2 minutes). Stir in cashews by hand.
Drop dough by level tablespoonfuls 2 inches apart onto ungreased cookie sheets. Bake for 10 to 12 minutes or until golden brown. Cool completely.
Melt 1/2 cup butter in heavy 1-quart saucepan over medium heat. Continue cooking, stirring occasionally, until butter foams and just starts to turn golden (4 to 6 minutes). (WATCH CLOSELY.) Immediately remove from heat. Pour into medium bowl; cool 5 minutes.
Add powdered sugar, milk and vanilla; beat until smooth. Frost cooled cookies. Top with cashew half, if desired.