Heat oven to 350°F. Line two 8-inch round baking pans with foil.
Beat butter, granulated sugar, brown sugar and vanilla until light and fluffy. Add egg; beat well. Stir together flour and baking soda; add to butter mixture, beating until blended. Stir in milk chocolate chips. Spread half of batter into each prepared pan, spreading to 1-inch from edge. (Cookies will spread to edge when baking.)
Bake 18 to 22 minutes or until lightly browned. Cool completely. Once cool, carefully lift cookies from pan and remove foil. Cut each cookie into 8 wedges (a pizza cutter works well); serve topped with scoop of ice cream or whipped cream, if desired.