For the pretzels, in the bowl of a stand mixer, combine water, sugar and salt. Sprinkle the yeast on top and let it sit for approximately 5 minutes or until it starts to foam
Add the hook attachment to the mixer. Add the flour and butter to the bowl and mix on low until combined. Increase to medium and knead until dough pulls away from the side of bowl, about 4 minutes.
Remove dough from bowl and spray bowl with cooking spray. Return dough to bowl, cover with plastic wrap and place in a warm place for 1 hour until doubles in size. I like to preheat oven to 170 degrees, place dough inside, turn the oven off and let is rest there.
While the dough is resting make the beer cheese. In a medium saucepan over medium heat, melt butter and whisk in flour.
Take mixture off heat and whisk in 2 tablespoons milk until smooth. Whisk in rest of milk and whisk until smooth.
Add beer, dijon mustard, garlic, salt and papika. Return pan to medium heat and stir until thick and bubbling, 2-3 minutes. Remove from heat.
Add grated cheese one cup at a time, whisking after each addition. Return to medium heat to melt cheese if needed.
When the dough has doubled, line two baking sheets with parchment paper or silpat mats. Preheat oven to 450 degrees.
Bring water and baking soda to a rolling boil. While it heats, turn dough out onto smooth surface and divide dough into 8 equal pieces. Roll out each piece evenly into a 20-22 inch rope. Cut dough in one inch pieces.
When water is boiling, drop dough into baking soda bath about 15 pieces at a time for 30 seconds. Remove with slotted spoon and place on prepared baking sheets. Repeat until all pretzel bites are complete. Dough will rise and become slightly cooked.
Whisk egg with 1 tablespoon water. Spread dough bites 1 inch apart and spread egg wash on top. Sprinkle with sea salt.
Bake 10-12 minutes until golden brown.