In a small bowl or glass measuring cup, add water and 1/2 cup milk. Microwave in 15 second increments, stirring each time, until the mixture is warm to the touch. It should be pleasant, not at all like you want to take your finger out. If it gets too hot, then stick it in the fridge for a couple minutes.
When the milk and water are nice and warm but not hot, add the yeast and stir. Set aside.
In a large bowl or stand mixer, add 1/4 cup softened butter. Add 3 tablespoons white sugar and the salt. Beat with the paddle. (Or with a wooden spoon)
Check the yeast. If it is looking bubbly, then it's ready to go. If it hasn't changed at all, then toss it and start over. Better to find out now than in 2 hours when your bread doesn't rise.
Add the yeast mixture and 2 eggs to bowl with the butter. Beat well.
Add the flour, one cup at a time. I added the full 3 and 1/2 cups but you may need to add less. It should form a fairly stiff dough that is smooth and does not stick to the sides of the bowl.
Knead with the dough hook or by hand for 5 minutes.
Spray a large bowl with nonstick spray. Shape the dough into a ball and put it in the bowl. Turn once so that the top is coated in oil, then cover the bowl with plastic wrap.
Let rise in a warm place for 1 and 1/2 hours.
When the dough has doubled in size, punch down.
Divide the dough in half.
On a lightly floured work surface or a pastry cloth
, roll one half into a 14x8 inch rectangle. It doesn't have to be perfect.
Make the filling: in a medium bowl, stir together 1/4 cup softened butter, brown sugar, 1/3 cup white sugar, maple syrup, flour, cinnamon and 1/2 teaspoon maple extract. Add the walnuts if you are using them.
Spread half of the filling on the dough.
Roll up the dough from the 14 inch edge, the long way, so you have one long strip rolled up. See photos.
Use wet fingers to pinch and seal the edges.
Use a sharp serrated knife to cut the roll in half lengthwise, all the way down the middle. See photos. I actually cut right along the seam I had just made.
Lay each half so that the filling side is facing up. Twist the strips of dough together, keeping the cut side facing up. Use wet fingers to pinch the ends together. You should have one long twist that is all sealed.
Spray 2 cake pans
with nonstick spray. They can be either 8 or 9 inch pans.
Coil the twisted dough into a circle in the prepared pan. Tuck the end underneath.
Loosely cover with plastic wrap that has been sprayed with nonstick spray. Put in a warm place to rise for another 45 minutes. The cakes should double in size.
Repeat the process with the other half of the dough.
When the cakes are almost done rising, turn the oven on to 350 degrees F.
Discard the plastic wrap at bake at 350 for 20-25 minutes. The top should be a deep golden brown and the center should be firm.
Remove from the oven and place on a wire rack to cool for 10 minutes. Set a timer! You don't want to forget. If you leave it in the pan too long you will have to battle with Maple Cement.
After 10 minutes, use a knife to loosen the edges of the pan, then use a spatula or two to help you lift the cake out of the pan onto a cooling rack.
In a small bowl, whisk together 1 cup powdered sugar, 1 tablespoon milk, and 1/2 teaspoon maple extract. Add a bit more milk if you prefer a thinner glaze.
Drizzle the glaze over the cakes.
Serve warm. If you are making these ahead, heat up individual portions in the microwave for about 10 seconds.