2 tablespoons Unsalted Butter, melted, for brushing after baking
In the bowl of a stand mixer fitted with a dough hook, or in a large bowl, mix together the flour, yeast, salt, 1 tablespoon of melted butter, brown sugar and 2 cups of very warm water. Once the ingredients are combined, knead for 5-6 minutes by machine, or 10-12 by hand.
The dough should clear the sides and bottom of the bowl and be very soft and smooth, but not overly sticky. If it’s too sticky add a bit more flour, a tablespoon at a time, if it’s really dry and not tacky at all, add a little more water a tablespoon at a time.
Move the dough to a lightly oiled bowl and let rest for 30-60 minutes, the bowl covered tightly with plastic wrap.
Preheat the oven to 500°F. Lightly spray a baking sheet with non-stick cooking spray and set aside. In a large bowl, stir together the cheddar cheese, ham and scrambled eggs.
On a lightly oiled surface, roll out the dough to an 18x16 inch rectangle. Slice the dough into twelve 6x4 inch rectangles. Spread about 1/2 cup of the egg mixture in the middle of each rectangle, leaving a one inch space on each of the long sides. Cut the long sides into 1-inch diagonal strips, and fold these strips over top of the filling, alternating sides to form a braid. Pinch the ends to seal the dough. Repeat with the rest of the dough rectangles.
In a wide, shallow bowl, whisk together the warm water and the baking soda. Dip each braided roll into the baking soda solution, turning it to coat (whisk it together again in between every couple rolls as the soda tends to settle quickly) and place it on the baking sheet. Sprinkle with coarse or kosher salt.
Bake the rolls for 10-12 minutes or until the rolls are golden brown. When they come out of the oven, brush with the melted butter. Serve warm. They are best immediately after baking them, but they also reheat well, and are very good cold, so there are options!