Melt the butter in a medium saucepan over medium heat. Add the flour and cook 1 minute. Whisk in the milk and cook until slightly thickened. Remove from heat and stir in the Monterey Jack cheese, poblano chiles, and season with salt and pepper, to taste.
Place the queso sauce into a bowl and sprinkle with chopped poblano.
Whisk together the mustards and honey, to taste, until combined. Let sit at least 30 minutes before serving.;
Line 2 half sheet pans with parchment paper and spray liberally with vegetable spray.
Combine the water, sugar, yeast, and butter in the bowl of a stand mixer and mix with the dough hook until combined. Let sit for 5 minutes.
Add the salt and flour and mix on low speed until combined. Increase the speed to medium and continue kneading until the dough is smooth and begins to pull away from the side of the bowl, about 3 to 4 minutes. If the dough appears too wet, add additional flour, 1 tablespoon at a time. Remove the dough from the bowl, place on a flat surface and knead into a ball with your hands.
Oil a bowl with vegetable oil, add the dough and turn to coat with the oil. Cover with a clean towel or plastic wrap and place in a warm spot until the dough doubles in size, about 1 hour.
Preheat the oven to 425 degrees F.
Bring the water to a boil in a small roasting pan over high heat and add the baking soda.
Remove the dough from the bowl and place on a flat surface. Divide the dough into 8 equal pieces, about 4 1/4 to 4 1/2 ounces each. Roll each piece into a long rope measuring 22 inches and shape: take the right side and cross over to the left. Cross right to left again and flip up. Boil the pretzels in the water solution, 2 at a time for 30 seconds, splashing the tops with the warmed water using a spoon. Remove with a large flat slotted spatula or a spider. Place 4 pretzels on each baking sheet, brush the tops with the egg wash and season liberally with the salt. Place into the oven and bake for 15 to 18 minutes until golden brown.
Remove to a baking rack and let rest 5 minutes before eating. Dip into desired sauces.