For the pretzel bites:
Combine water, sugar, salt and yeast in bowl of stand mixer fitted with paddle attachment. Mix on low speed to dissolve yeast. Add flour and melted butter and mix just until dough comes together. Switch to dough hook and knead on medium speed until dough is smooth and elastic, about 5 minutes. Transfer dough to lightly buttered bowls, turning once to coat. Cover with plastic wrap and let rise in warm place, about 1 hour or until doubled in bulk.
Heat oven to 450°F. Line two baking sheets with parchment paper.
Bring water and baking soda to boil in large saucepan or stockpot.
Meanwhile, turn dough out onto lightly floured work surface and gently deflate it. Pat dough down into flat round about 1-inch thick. Use pizza cutter to slice the dough in strips in one direction and then perpendicularly to make 1-inch chunks.
Place pretzel bites into boiling water in batches so that they aren’t overcrowded. Boil each batch for about 30 seconds, stirring once or twice to submerge all surfaces. Remove from water with slotted skimmer and spread out on prepared baking sheets. Once all pretzels have been boiled, brush tops with egg wash and sprinkle lightly with salt. Bake until dark golden brown, about 9-11 minutes.
For the sauce:
Melt butter in small saucepan over medium high heat. Whisk in flour and garlic and cook until golden, about 1-2 minutes. Gradually whisk in milk. Cook, stirring often, until mixture thickens and bubbles. Stir in cheddar and season with salt and pepper to taste. If desired, process sauce with an immersion blender or in a food processor to make it extra smooth. Serve immediately with warm pretzel bites.