Beat zest of 1 lemon, zest of 1 orange, 4 Tbsp. unsalted butter, room temperature, ¼ cup granulated sugar, 1 tsp. anise liqueur (if using), 1 tsp. dark rum (if using), 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, 1 tsp. orange extract, 1 tsp. vanilla extract, and ½ tsp. lemon extract in the bowl of a stand mixer fitted with the paddle attachment on medium speed until pale and creamy, about 4 minutes. Add 1 large egg, room temperature, and beat until combined (it’s okay if mixture looks curdled).
Switch to the dough hook and add ⅔ cup whole milk, room temperature, ¼ cup fresh orange juice, 2 tsp. instant yeast, and 3 cups (375 g) all-purpose flour. Mix on low speed, scraping bottom and sides of bowl once or twice, until a smooth, soft dough forms, 18–20 minutes (toward the end of mixing, dough will release cleanly from the sides of bowl but may still stick to bottom).
Transfer dough to a surface and form into a ball. Lightly coat mixer bowl with vegetable oil, then return dough to bowl. Cover with plastic wrap or a plate and let dough rise in a warm spot until nearly doubled in size, 2–3 hours. Chill dough at least 30 minutes to firm up.
Turn dough out onto a lightly floured surface and pat into a square. Roll out to a 13×9″ rectangle, then rotate dough so a long side is closest to you. Using a bench scraper or knife, cut dough vertically into 8 strips. Gently roll up each strip into a coil (don’t roll too tight or the centers will pop out while proofing).
Lightly coat a 9″-diameter cake pan with oil. Arrange dough coils, cut side down, in pan, starting in the center, then working around the perimeter. Cover with plastic wrap or a plate and let dough rise in a warm spot until nearly doubled in size, 1–2 hours.
Place a rack in middle of oven and preheat to 350°. Uncover pan and bake bread until the center of each coil is golden brown (an instant-read thermometer inserted into the center of bread should register 190°), 23–28 minutes. Let cool in pan 15 minutes, then unmold fuatha and transfer to a wire rack set inside a rimmed baking sheet. Let cool completely, about 45 minutes.
Do ahead: Dough can be made 1 day ahead. Keep chilled after first rise.
Glaze and assembly
Whisk 1⅓ cups (147 g) powdered sugar, sifted, 3 Tbsp. honey, 1 Tbsp. fresh lemon juice, and a pinch of kosher salt in a small bowl until smooth.
Pour glaze over fuatha, scraping bowl with a rubber spatula to get every bit; spread evenly over top, letting it drip down the sides. Decorate with sprinkles as desired. Let sit until glaze is set, about 2 hours.