1. In a small pan, lightly crush anise seeds and allspice with a wooden spoon. Add 1/4 cup water and bring to a boil over high heat. Remove from heat and let steep 15 to 30 minutes, then pour through a fine wire strainer; reserve liquid and discard spices.
2. In another small pan over medium-low heat, combine butter, milk, and salt. Heat just until warm (110°; butter doesn't need to melt completely). Stir in sugar. The temperature may continue to rise even off the heat; if it gets too hot, let cool before adding to yeast mixture.
3. In the bottom of a large bowl, combine yeast and 1/4 cup warm (110°) water; let stand until yeast is dissolved, about 5 minutes.
4. Reserve 1 tablespoon of the beaten eggs; cover and chill. Add remaining beaten eggs, spice-infused water, and butter mixture to yeast mixture; stir until well blended. Stir in 2 cups flour. With a heavy-duty electric hand or standing mixer on medium speed, beat until dough is stretchy, 6 to 10 minutes, scraping it down if it rises up beaters.
5. If using a heavy-duty mixer with a dough hook, beat in 2 1/4 more cups flour on low speed until well blended. Then beat on medium speed, gradually adding just enough of the remaining 3/4 cup flour needed, until dough is smooth and no longer sticky, 6 to 10 minutes.
If kneading by hand, with a wooden spoon, stir in 2 1/4 more cups flour until blended. Dust board generously with some of the remaining 3/4 cup flour. Scrape dough onto the board and knead, adding just enough of the remaining flour needed to prevent sticking, until dough is smooth and no longer sticky, 10 to 15 minutes. Return dough to bowl.
6. Cover bowl with plastic wrap and let dough rise in a warm (70° to 80°) place until doubled, 1 1/2 to 2 hours.
7. Preheat oven to 350° (325° for convection heat). Punch dough down and knead briefly on a lightly floured board to release air. Shape into a smooth round and place in a buttered 10-inch cheesecake pan with removable rim at least 2 inches tall; press dough lightly to fill pan. Set 1 hard-cooked egg in the center and 4 eggs around edge, at the points of a cross. Cover pan lightly with plastic wrap and let rise in a warm (70° to 80°) place just until almost doubled, 35 to 50 minutes.
8. Brush bread with reserved beaten egg and sprinkle evenly with sesame seeds. Bake until bread is richly browned and a wooden skewer inserted in the center comes out clean, about 45 minutes. Let cool on a rack about 10 minutes, then run a knife around pan rim and remove; remove pan bottom. Let bread cool on rack at least 30 minutes. Cut into wedges to serve.
Note: Nutritional analysis is per serving.
Notes: In step 4, if you don't have an electric mixer, stir in flour with a spoon until blended, then proceed to step 5. Knead at least 15 minutes. You can make this bread up to a day ahead; cover and store at room temperature (but don't eat the eggs the next day). To reheat, wrap loaf loosely in foil and bake in a 350° oven until warm, 10 to 15 minutes.