In the bowl of a stand mixer, whisk together 1 cup (125 grams) of all-purpose flour, granulated sugar, instant yeast, kosher salt, ground cardamom, and ground cinnamon by hand until combined.
In a medium saucepan, combine ⅔ cup (160 grams) of whole milk, 6 tablespoons (84 grams) of unsalted butter, and ⅓ cup (80 grams) of water; cook over medium-low heat, stirring occasionally, until the butter is melted and the temperature registers between 120°F (49°C) to 130°F (54°C).
Add the warm milk mixture to the flour mixture. Using the paddle attachment, beat at medium-low speed until combined, about 1 minute, stopping to scrape sides of bowl.
Add one large egg (50 grams) and beat at medium-low speed until combined, about 1 minute.
With the mixer on low speed, gradually add 2½ cups (313 grams) of all-purpose flour, mixing until combined.
Switch to the dough hook attachment. With the mixer on low speed, beat until a soft, slightly sticky, and elastic dough forms, about 8 to 12 minutes.
With the mixer on low speed, gradually add the candied orange peel, raisins, and dried sweetened cranberries, mixing just until combined.
Spray a large bowl with cooking spray. Place the dough in the bowl and turn to grease the top. Cover and let rise in a warm, draft-free place until doubled in size, about 35 to 50 minutes.
Punch down the dough gently to remove excess air and let it stand for 10 minutes.
On a lightly floured surface, divide the dough into three equal portions (about 340 grams each). Shape each portion into a ball, cover and let stand for 15 minutes.
Take one portion seam side up. Flatten it into a 9x5-inch oval. Starting from one long side, fold the dough over about ½ inch at a time, pressing to seal after each fold. Roll the cylinder into a 12-inch rope.
Braid the three ropes together, pinching the ends to secure them and tucking them under slightly.
Spray a 9x5-inch loaf pan with cooking spray and place the braided dough inside, pressing to create an even layer. Cover and let rise until doubled in size, about 35 to 40 minutes.
Preheat your oven to 350°F (180°C). In a small bowl, whisk together the remaining egg and another tablespoon of milk. Brush the top of the dough with this egg wash.
Bake for 12 minutes, then loosely cover with foil and rotate the pan. Continue to bake until golden brown, about 38 more minutes.
Once baked, remove from the pan and cool completely on a wire rack. Drizzle with sugar glaze and enjoy.
