Heat oven to 350°F.
Combine brown sugar, 3/4 cup butter and water in heavy 3-quart saucepan. Cook over medium heat, stirring occasionally, 3-4 minutes, until butter is melted. Add chocolate chips; cook, stirring constantly, 1-2 minutes, until chocolate is melted and smooth. Remove from heat. Beat in 1 egg at a time, until mixture is smooth. Stir in all remaining cookie ingredients.
Drop dough by rounded teaspoonfuls onto ungreased cookie sheets. Bake 6-8 minutes or until set. Let stand 1 minute; remove from cookie sheets. Cool completely.
Combine all filling ingredients except milk in mixer bowl. Beat at low speed, scraping bowl often and gradually adding enough milk for desired spreading consistency.
Spread about 2 teaspoons frosting onto flat-side of one cookie; top with second cookie, flat-side down. Squeeze together gently. Repeat with remaining cookies.
VARIATION: Chocolate Mint Sandwich Cookies. Prepare cookies as directed above. Substitute 1/8 teaspoon peppermint or mint extract for vanilla in filling.