In a food processor, combine butter, granulated sugar, and salt. Cover and process until smooth. Add milk, egg, egg yolk, rum, lemon peel, lemon juice, and orange peel. Cover and process until smooth. Scrape bowl. Add flour. Cover and pulse with several on/off turns until dough is smooth and thoroughly combined. Transfer dough to a lightly floured surface and knead, adding additional flour as needed until dough is soft but not sticky. Form dough into a ball and wrap in plastic wrap. Chill for at least 30 minutes or until dough is easy to handle. Or chill overnight and let dough stand at room temperature for 10 minutes before rolling.
Divide dough into two portions. On a lightly floured surface, roll half of the dough into a 16-inch square, turning dough and adding flour to the work surface as needed. With a fluted cutter, cut the dough into 10 strips, about 11/2 inches wide. Cut strips in half crosswise to make 20 strips. Tie each strip with a knot in the center. Transfer dough knots to a baking sheet lined with waxed paper. Repeat with other dough portion.
In a large saucepan or deep-fryer, heat oil to 350 degrees F. Fry eight dough knots at a time in the hot oil for 4 minutes or until crostoli are golden brown, turning halfway through cooking time. Drain on paper towels. Repeat with remaining dough knots. Cool completely. Sprinkle with powdered sugar before serving.
Makes 40 servings
Make-ahead tip: Freeze cooled crostoli the same day they are fried. Place in a resealable plastic freezer bag and freeze for up to 1 month. Sprinkle with powdered sugar before serving.