In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugar, baking powder, and salt. Beat until combined, scraping sides of bowl occasionally. Beat in egg, orange peel, orange juice, and anise extract until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour. Cover and chill about 1 hour or until dough is easy to handle.
Preheat oven to 350 degrees F. Line a cookie sheet with parchment paper. Shape dough into 1-inch balls. Place balls 1 inch apart on the prepared cookie sheet. If desired, flatten balls to about 1/2 inch thick.
Bake about 10 minutes or until bottoms are light brown. Transfer cookies to a wire rack; cool.
Spread tops of cookies with Blood Orange Frosting. Sprinkle with Candied Citrus Threads.
Candied Citrus Threads
Using a citrus zester, remove blood orange peel in threadlike pieces. In a small saucepan combine orange peel and enough water to cover. Bring just to boiling over medium-high heat; reduce heat. Simmer for 5 minutes; drain. In the same saucepan combine 1-1/2 cups sugar and the 1-1/2 cups water. Bring just to boiling over medium-high heat, stirring to dissolve sugar. Stir in orange peel; reduce heat. Simmer for 8 to 10 minutes or until peel is tender; drain well. Sprinkle a large shallow pan with enough sugar to cover lightly. Sprinkle orange peel evenly over sugar. Let stand until dry and brittle.
Blood Orange Frosting
In a medium mixing bowl beat butter with an electric mixer on medium speed until smooth. Gradually add about half of the powdered sugar, beating well. Beat in 3 tablespoons of the milk, the orange peel, and vanilla. Beat in the remaining powdered sugar. If necessary, beat in enough of the remaining milk, 1 teaspoon at a time, to reach spreading consistency. Makes 1-1/2 cups.