PREHEAT oven to 350º F. Line two baking sheets with parchment paper or lightly grease.
COMBINE flour, baking soda and salt in small bowl. Beat butter and sugar in medium mixer bowl on medium speed until light and fluffy. Beat in milk, egg and vanilla extract (mixture will be thin.) Beat in flour mixture on low speed until smooth. Stir in morsels. Drop by heaping measuring teaspoonfuls onto prepared baking sheets. A total of 36 cookies are needed for the recipe.
BAKE for 12 to 14 minutes until springy to the touch. Cool completely on baking sheets.
FOR CHOCOLATE MARSHMALLOW FILLING:
MICROWAVE morsels in uncovered, medium microwave-safe mixer bowl on HIGH (100%) power for 30 seconds; STIR. The morsels may retain some of their original shape. If necessary, microwave at additional 10- to 15-second intervals, stirring just until morsels are melted.
ADD marshmallow crème and butter to melted chocolate. Beat on medium speed until smooth. Transfer filling to resealable plastic bag. Cut hole from corner of bag. Squeeze heaping tablespoon of filling onto flat side of one cookie, top with flat side of second cookie to make a sandwich. Repeat with remaining cookies and filling. Store in covered container in refrigerator.