Preheat oven to 350F (175C) and line several baking sheets with parchment paper. Set aside.
In a large mixing bowl, combine butter and sugar and cream together with an electric mixer until light and fluffy.
Add eggs, anise extract, and vanilla extract and use mixer on low-speed to stir well.
In a separate, medium sized mixing bowl, whisk together flour, baking powder, and salt.
Gradually (in 3-4 parts) add dry mixture into butter mixture, stirring until completely combined after each addition.
Scoop dough into 1 Tablespoon-sized scoop, round dough by rolling gently between your palms, and place on baking sheet, spacing cookies at least 2” (5cm) apart.
Bake cookies in 350F (175C) oven for 8-9 minutes. The bottoms of the cookies should be very lightly browned but the tops should still be pale. Allow cookies to cool on baking sheet for several minutes before transferring to cooling rack to cool completely.
To prepare the glaze/icing, whisk together sugar, milk, corn syrup, and extracts until smooth. Frosting should have a ribbon consistency, if it is too thick add more milk, a small bit at a time.
Drizzle icing over completely cooled cookies. If desired, sprinkle with nonpareils before icing hardens. Allow frosting to set before enjoying.