Put vinegar in a 1-cup measure; add evaporated milk and set aside.
Beat butter until light; add brown sugar and beat until mixture is light and fluffy. Beat in eggs and vanilla to blend thoroughly.
Sift together flour, baking soda, baking powder and salt.
Stir evaporated milk and add alternately with dry ingredients to creamed mixture. Stir in chopped nuts. Drop rounded tablespoonfuls of dough about 2½" apart onto lightly greased baking sheet.
Bake in moderate oven (350°) 10 to 12 minutes, or until lightly browned and barely firm to touch. Remove cookies and cool on racks. When cool, spread with Brown Butter Frosting and press a walnut or pecan half in each cookie.