In the bowl of a stand mixer fitted with the paddle attachment, beat 1 cup (127 grams) flour, ⅓ cup (67 grams) sugar, yeast, salt, ¾ teaspoon (1.5 grams) cardamom, and ¼ teaspoon ginger at low speed until combined.

In a medium saucepan, heat milk, ¼ cup (57 grams) butter, and oil over medium heat, stirring frequently, until butter is melted and an instant-read thermometer registers 120°F (49°C) to 130°F (54°C). Add warm milk mixture to flour mixture; beat at medium-low speed for 2 minutes, stopping to scrape sides of bowl. Add Milk Roux, eggs, and orange blossom water; beat at medium-high speed for 2 minutes. With mixer on low speed, gradually add 2¼ cups (286 grams) flour, beating just until combined.

Switch to the dough hook attachment. Beat at medium-low speed until a soft, tacky dough forms, 6 to 10 minutes, stopping to scrape sides of bowl; add up to remaining ½ cup (64 grams) flour, 1 tablespoon (8 grams) at a time, if dough is too sticky. (Dough may still stick slightly to sides of bowl but should pass the windowpane tests see Notes.)

Add candied orange and anise seeds to dough, and beat at low speed just until combined. Turn out dough onto a very lightly floured surface; knead 6 to 10 times to help disperse candied orange and anise seeds.

Lightly spray a large bowl with cooking spray. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 40 minutes to 1 hour.

Punch down dough; cover and let stand for 5 minutes. Turn out dough onto a clean surface; divide into 10 portions (about 96 grams each), and shape into balls, pinching seams closed as needed. Cover with plastic wrap, and let stand for 10 minutes.

Position oven rack in upper third of oven. Preheat oven to 375°F (190°C). Line 2 light-colored baking sheets with parchment paper.

Flatten and shape each ball into a 4×4-inch semicircular shape. With flat side closest to you, use a plastic bench scraper, make a 2½-inch-long cut crosswise in center of semicircle. Make a 2½-inch-long cut on each side of first cut, angled toward center of flat portion of semicircle, leaving about ¼ to ½ inch of dough intact on each side. Along rounded side of semicircle, make 1-inch cuts evenly spaced to side of each original cut. Stretch dough gently to open cuts; place on prepared pans. Cover and let rise in a warm, draft-free place (75°F/24°C) until dough is puffed and holds an indentation when poked, 25 to 30 minutes.

Bake, one batch at a time, until lightly golden, 8 to 10 minutes.

In a small microwave-safe bowl, heat remaining ½ cup (113 grams) butter on high in 10-second intervals, stirring between each, until melted.

In a medium bowl, stir together remaining 1⅓ cups (267 grams) sugar, remaining ¼ teaspoon ginger, and remaining ⅛ teaspoon cardamom.

Brush warm loaves on both sides with melted butter. Roll each loaf in sugar mixture twice. Serve warm, or let cool completely on wire racks.