In the bowl of a stand mixer, whisk together 1 cup (125 grams) fl our, sugar, yeast, salt, cardamom, and cinnamon by hand until combined.

In a medium saucepan, combine ⅔ cup (160 grams) milk, butter, and ⅓ cup (80 grams) water; cook over medium-low heat, stirring occasionally, until butter is melted and an instant-read thermometer registers 120°F (49°C) to 130°F (54°C). Add warm milk mixture to fl our mixture; using the paddle attachment, beat at medium-low speed until combined, about 1 minute, stopping to scrape sides of bowl. Add 1 egg (50 grams); beat at medium low speed until combined, about 1 minute, stopping to scrape sides of bowl. With mixer on low speed, gradually add 2½ cups (313 grams) flour, beating until combined.

Switch to the dough hook attachment. With mixer on low speed, beat until a soft, slightly sticky, and elastic dough forms, 8 to 12 minutes, stopping to scrape sides of bowl and dough hook; add up to remaining ¼ cup (31 grams) fl our, 1 tablespoon (8 grams) at a time, if dough is too sticky. (Dough may still stick to sides and bottom of bowl but should pass the windowpane test; see Note.) With mixer on low speed, gradually add orange peel, raisins, and cranberries, beating just until combined. (If you do not feel the mix-ins are well distributed by the mixer, you can use your hands to fold and squeeze the dough to help distribute the mix-ins more evenly.)

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, 35 to 50 minutes.

Punch down dough; cover and let stand for 10 minutes. On a very lightly floured surface, divide dough into 3 portions (about 340 grams each). Shape each portion into a ball, and gently roll between your hands to create a roughly oval shape; cover and let stand for 15 minutes. Place 1 portion seam side up. Flatten portion into about a 9x5-inch oval, making sure to press out and pop any air bubbles. Starting from one long side, fold dough, about ½ inch at a time, pressing to seal after each fold. Repeat until you have a tight cylinder. Roll cylinder into a 12-inch rope. Repeat with remaining portions. Braid ropes, pinching ends together and tucking under slightly to secure.

Spray a 9x5-inch loaf pan with cooking spray. Place braided dough in prepared pan; gently press braid into an even layer in pan. Cover and let rise in a warm, draft free place (75°F/24°C) until doubled in size, 35 to 40 minutes. (It is OK if dough is puffed above rim of pan.)

Preheat oven to 350°F (180°C).

In a small bowl, whisk together remaining 1 egg (50 grams) and remaining 1 tablespoon (15 grams) milk. Brush top of dough with egg wash. (If any larger bubbles appear on dough’s surface, gently pierce and deflate before egg washing.)

Bake for 12 minutes; loosely cover with foil, and rotate pan. Bake until golden brown and an instant-read thermometer inserted in center registers 190°F (88°C), to 38 minutes more. Remove from pan, and let cool completely on a wire rack.

Drizzle cooled loaf with Sugar Glaze. Store in a bread box or a somewhat airtight container at room temperature for 2 to 3 days.