There's no need to use a pastry bag to fill cookies. Just transfer the frosting to a zip-top plastic freezer bag, and snip the corner.
Preheat oven to 325°. Beat butter and sugar at medium speed with an electric mixer until creamy. Add egg and food coloring; beat 30 seconds.
Sift flour with next 2 ingredients in a small bowl. Add flour mixture to butter mixture, beating at low speed until combined. Stir in vanilla.
Shape dough into 1-inch balls, and place 1/2 inch apart on parchment paper-lined baking sheets. Press thumb or end of a wooden spoon into each ball, forming an indentation.
Bake at 325° for 10 to 15 minutes or until cookies are fragrant and dry. While cookies are still warm, press indentations again. Cool cookies completely on a wire rack (about 30 minutes).
Stir together cream cheese and melted white chocolate in a small bowl. Fill centers of cookies with cream cheese mixture.
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