In large bowl, combine brown sugar and 1 cup butter; beat until light and fluffy. Add egg; blend well. Add flour, cardamom and cinnamon; mix well. If necessary, cover with plastic wrap; refrigerate 1 hour for easier handling.
Heat oven to 350°F. Shape dough into 1-inch balls; roll in sugar. Place 2 inches apart on ungreased cookie sheets. For each cookie, dip bottom of glass that has textured base in sugar; flatten dough ball to form 1 1/2-inch round.
Bake at 350°F. for 6 to 10 minutes or until firm to the touch. Immediately remove from cookie sheets. Cool 15 minutes or until completely cooled.
Melt 2 tablespoons butter in medium saucepan over medium heat; cook until light golden brown. Remove from heat. Stir in all remaining filling ingredients, adding enough milk for desired spreading consistency. For each sandwich cookie, spread about 1 teaspoon filling between 2 cooled cookies.