Step 1
Combine warm water sugar and salt in the bowl of a stand mixer and sprinkle yeast on top. Let sit until mixture begins to foam about 5 minutes. Add flour and butter. Mix on low using the dough hook attachment. Increase speed slightly and knead until dough is smooth and pulls away from the sides of the bowl 4 to 5 minutes.
Step 2
Grease a large bowl with cooking spray. Shape dough into a ball and place in the bowl. Cover with plastic wrap and let sit in a warm place until doubled in size about 1 hour.
Step 3
Transfer the dough to a lightly greased work surface and cut into 8 equal pieces.
Step 4
Preheat the oven to 450 degrees F (232 degrees C). Line 2 sheet pans with parchment paper and spray with cooking spray. Bring water to a boil in a large pot for the baking soda bath.
Step 5
Roll each piece of dough into thin rope about 18 to 20 inches long and 1-inch thick. Form into a U shape. Cross the ends over each other toward the center of the U twist again and press into the U. Place pretzels on the prepared sheet pans.
Step 6
Pour baking soda into the boiling water. Boil pretzels one at a time for 30 seconds each. Return them to the parchment paper using a wide slotted spoon. Mix egg with a splash of water and brush onto the pretzels; sprinkle with salt.
Step 7
Bake in the preheated oven rotating pans halfway through until golden brown 12 to 14 minutes. Transfer pans to wire cooling racks. Brush pretzels with multiple layers of melted butter while still hot.
Step 8
Melt American cheese and milk together in a bowl set over a pot of simmering water.
Step 9
Meanwhile heat olive oil in a skillet over medium heat. Add onion garlic cumin and salt; cook until fragrant and soft 3 or 4 minutes. Mix onion mixture into the melted cheese along with diced tomatoes and green chiles. Stir in more milk if queso seems too thick. Serve dip with pretzels for dipping.