Pour beer and water into microwave safe bowl and microwave for 20-30 seconds to make just slightly warm, around 110° F.
Combine the beer, water, sugar and yeast in bowl of stand mixer and allow to sit for 5 minutes.
Add the butter, salt and flour to the mixture and mix on low speed with dough hook 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 4 to 5 minutes. If the dough appears is wet, add more 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.
Place in a large greased mixing bowl. Cover and let the dough rest in a warm area until it has doubled in size, about 1 hour.
Preheat oven to 425°F. Line two large baking sheets with parchment paper and set aside.
Divide the dough into 6 equal pieces. Roll the dough into six 20-inch long ropes. Cut the rope into 1.5 inch pieces to make the bites.
Add 9 cups of water and baking soda to a large pot and bring to a boil. Drop 10 bites at a time and boil for a quick 30 seconds. Remove with a slotted spoon and place on prepared baking sheet. Repeat with remaining pretzel bites.
Making sure the bites aren't touching, brush each with some beaten egg and sprinkle with sea salt. Bake for 15-18 minutes or until golden brown. Serve with cheese dip.