Make dough: In the bowl of a stand mixer, whisk together lukewarm water and yeast until dissolved. Add 1 cup (125 grams) flour; using the paddle attachment, beat at low speed until a stiff dough forms. (If flour is not incorporated, knead dough in bowl by hand until it is combined; scrape bowl as needed.) Cover and let flour mixture stand in a warm, draft-free place (75°F/24°C) until doubled in size, about 15 to 20 minutes.
Add 2 cups (250 grams) flour, granulated sugar, salt, and anise seed to flour mixture. Add eggs, lukewarm milk, vanilla, and orange zest. Beat at low speed until a shaggy dough forms; scrape sides of bowl.
Switch to the dough hook attachment. Beat at low speed until dough is tacky, soft, smooth, and elastic, 6 to 8 minutes; add up to remaining ¼ cup (31 grams) flour, 1 tablespoon (8 grams) at a time, if dough is too sticky. Add butter, 1 tablespoon (14 grams) at a time, beating until combined after each addition (3 to 4 minutes total). After all the butter is incorporated, knead until a soft, smooth, and elastic dough forms, about 5 to 7 minutes. Turn out dough onto a lightly floured surface, and shape into a smooth round.
Bulk rise: Lightly oil a large bowl. Place dough in bowl, turning to grease top. Cover and refrigerate overnight.
Prepare Fruit Mixture: In a medium bowl, stir together candied orange, raisins, liqueur, cherries, cranberries, and remaining ⅓ cup (80 grams) water. Cover and let stand overnight.
Lightly spray 2 (6-well) popover pans with baking spray with flour. Line wells with tulip-style paper baking cups (see note 2).
Drain fruit mixture; pat dry with paper towels.
Shape buns: On a heavily floured surface, roll dough into a ½-inch-thick oval (about 12x10 inches). Sprinkle half of the fruit mixture onto dough. Using a rolling pin, press fruit into dough. Fold dough in half lengthwise. Rotate dough 90 degrees. (Wipe off any liquid from fruit, and re-flour rolling pin if needed.) Roll dough into a ½-inch-thick oval. Sprinkle with the remaining fruit. Press fruit into dough; fold dough in half lengthwise. Rotate dough 90 degrees and roll into a ½-inch-thick oval. Divide dough into 12 portions (about 93 grams each). Using the palm of your hands, gently roll each portion into a smooth ball, lightly flouring your hands as needed. Place dough in prepared wells.
Final rise: Cover with lightly greased plastic wrap, and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, about 1½ hours.
Preheat oven to 375°F (190°C).
Topping: In a small bowl, beat egg; gently brush onto risen buns. Sprinkle pearl sugar evenly over buns.
Bake: Bake for 5 minutes. Reduce oven temperature to 350°F (180°C) and bake until golden brown and an instant-read thermometer inserted in center registers 190°F (88°C), about 10 to 12 minutes more. Let cool in pan for 5 minutes. Remove from pan and let cool completely on a wire rack. Store in an airtight container for up to 3 days.