Orange-blossom water adds a citrus perfume to this dough. Look for it in specialty food stores or order it online.
Combine flour, 3/4 cup sugar, salt, and baking powder in a large bowl. Mix together butter, orange-blossom water, vanilla and anise extracts, and egg in another bowl. Pour into flour mixture. Mix well, adding ice water, 1 tablespoon at a time, until dough is stiff but not crumbly.
Roll out dough to 3/8-inch thickness on a lightly floured cutting board. Cut dough into 3/8-inch-wide strips, then cut crosswise into 3/8-inch squares. Roll each piece into a ball, transferring to a lightly floured surface as you work.
Heat 2 inches oil in a medium heavy saucepan until a deep-fry thermometer registers 375 degrees. Working in batches, fry dough, stirring, until golden. Remove fried dough from oil using a wire-mesh skimmer, and transfer to paper towels to drain.
Heat honey, remaining 3 tablespoons sugar, and 3 tablespoons water in a small saucepan until sugar dissolves. Working in batches, dip struffoli in honey sauce until well coated, and transfer to a sieve set over a bowl to drain; reserve honey sauce. Mound struffoli on a platter, pour remaining and reserved honey sauce over top, and sprinkle with almonds and nonpareils.