BEAT butter, granulated sugar and vanilla extract in large mixer bowl until creamy. Gradually beat in flour. Cover; refrigerate for 1 hour.
PREHEAT oven to 350° F.
SHAPE dough into 1-inch balls; place 2 inches apart on ungreased baking sheets. Press thumb into tops to make 1/2-inch-deep depressions (dough will crack around edges). Fill each depression with about 1/4 teaspoon jam.
BAKE for 14 to 16 minutes or until edges are lightly browned. Immediately press 1 Nestlé NestEgg into center of each cookie. Cool cookies on baking sheets for 2 minutes; remove to wire racks to cool completely.
COMBINE powdered sugar, 1 tablespoon butter and milk in small mixer bowl; whisk until smooth. Add more milk if needed. Drizzle over tops of cookies.