To make the dough:

1. In a large stand mixer, combine warm water, warm milk, and yeast. Let sit for about 8 minutes, stirring occasionally, until yeast is completely dissolved.
2. Add flour and salt to the bowl. Beat using a paddle attachment on medium-low speed until a shaggy dough starts to form, scraping down the sides when needed, about 1–2 minutes. With the mixer running, add eggs one at a time, until the dough loosens. Beat in sugar, scraping down sides when needed.
3. Increase speed to medium and beat until the dough becomes smooth, about 2–3 minutes.
4. Change mixer speed to low. Add butter 1 tablespoon at a time until mostly incorporated. Continue until all butter has been used and the dough is soft, about 4 minutes. Turn speed to medium-high and beat until dough starts to form a ball, about 6–8 minutes.
5. Butter the sides of a large bowl. Transfer dough to bowl and cover with plastic wrap. Let rise for 1 hour 15 minutes, until about doubled in size.
6. Gently deflate the dough by lifting the edges from around the bowl and flipping it over. Cover the bowl with plastic wrap and let sit for 30 more minutes. Repeat the deflate-and-rise procedure 3 more times (total rise time: 3 hours 15 minutes).

To make the filling:

1. While the dough is rising, make the filling. Using a stand mixer, beat together the butter, brown sugar, cardamom, cinnamon, nutmeg, orange zest, and almond extract until creamy and smooth, about 3 minutes. If the mixture feels too clumpy, add an extra tablespoon of butter. Set aside until the dough is ready.

To assemble:

1. On a lightly floured surface, roll out the dough into a large rectangle, about 1/4 inch thick. Spread the cardamom filling evenly across the dough, staying about 1/2 inch from the edges.
2. Starting with the longer side, roll the dough into a log. Trim about 1 inch off each end and discard the scraps.
3. Using a sharp knife, gently cut the dough in half lengthwise to expose the filling. Place cut-sides facing up and pinch together one end of the two strands to start the braid. Lift the right strand over the left strand and repeat until you reach the end. Pinch ends together.
4. Gently transfer the dough to a 9 by 5-inch bread pan. Cover with plastic wrap and let rise for 1 hour.
5. While the dough is on its final rise, preheat oven to 350°F.
6. Remove plastic and bake for 35–45 minutes, until a toothpick inserted into the center comes out clean. Let cool slightly.
7. While the loaf is cooling, combine the sugar and water for the glaze in a small saucepan. Bring to a boil, stirring occasionally, until sugar is dissolved. Using a pastry brush, brush the glaze all over the top of the loaf. Serve warm or let cool completely.