To make the pretzels: In the bowl of a stand mixer fitted with the paddle attachment, mix together the water, sugar, yeast, and salt on low speed for 10 seconds. Switch to the dough hook and add the flour and butter. Mix on low speed until well combined. Change to medium speed and knead until the dough is smooth and pulls away from the side of the bowl, approximately 4 to 5 minutes. Remove the dough from the bowl and transfer it to a well-oiled bowl. Cover the bowl tightly with plastic wrap and set it in a warm place for approximately 50 to 55 minutes or until the dough has doubled in size.
Preheat the oven to 425 degrees F. Line 2 large baking sheets with parchment paper. Set aside.
Bring the 10 cups of water and the baking soda to a rolling boil in an wide 8-quart saucepan or roasting pan.
In the meantime, turn the dough out onto a slightly oiled work surface and divide into 8 equal pieces. Roll out each piece of dough into a 24-inch rope. Slice each rope into 1 1/2-inch pieces. Place a lightly damp towel over the pretzel pieces to prevent them from drying out while you roll and cut the other pieces.
Using a slotted spoon lower a handful of the pretzel pieces into the boiling water and boil them for 30 seconds, flipping them around in the water with the spoon a couple of times. Remove the pretzel pieces from the water using the spoon, drain as best you can, and place them on the baking sheets. Brush the top of each pretzel with the melted butter and sprinkle with the pretzel/Kosher salt. Bake until dark golden brown in color, approximately 10 - 12 minutes. Brush with remaining melted butter before serving. Serve warm.
To make the cheese sauce: In a small saucepan set over medium heat, melt the butter. Whisk in the flour and cook for 30 seconds, whisking constantly.
Slowly whisk in the milk until no lumps of flour remain. Stirring constantly, bring the milk to a simmer over medium-low heat until it thickens, about 3-5 minutes. Remove the pan from the stove and stir in the shredded cheese until all of the cheese has melted. Add a pinch of salt, if needed. Serve warm. Leftovers can be reheated in the microwave on medium power at 30 second intervals.