1Warm the milk and water in a small microwave-safe bowl for approximately 45 seconds.
2Add granulated sugar and instant yeast to the warm milk/water mixture, mix quickly, and let it sit for 5-8 minutes until the yeast blooms.
3In the bowl of a stand mixer, whisk together bread flour, brown sugar, salt, baking powder, and partially melted butter.
4Attach the dough hook to the stand mixer, add the bloomed yeast mixture to the dry ingredients, and mix on low speed until a dough ball forms.
5Sprinkle bread flour on a clean, dry counter and place the dough ball on top.
6Knead the dough by hand for about 3 minutes until it is slightly sticky and soft.
7Form the dough into a tight ball and place it in a well-oiled bowl.
8Cover the bowl with plastic wrap and a warm kitchen towel, allowing the dough to rise for 45 minutes to 1 hour, or until it has doubled in size.
9Line a baking sheet with parchment paper and preheat your oven to 400℉ (200°C).
10After the first rise, place the dough back onto a lightly floured counter and gently roll it out using a rolling pin.
11Cut the dough into 6 equal strips.
12Roll each strip out to about 22 inches long.
13Cut 1-inch pieces from the dough strips.
14In a medium mixing bowl, combine warm water and baking soda for the water bath.
15Dunk all the dough pieces into the water bath for a few seconds, then remove them, strain excess water, and place them on the baking sheet.
16Bake at 400℉ (200°C) on the center rack for 8-9 minutes until the tops are slightly golden and the bottoms are a deeper brown, keeping an eye on them as baking times may vary.
17Allow the pretzel bites to cool.
18Melt 5 tablespoons of butter.
19Divide the pretzel bites into two separate mixing bowls if making both salted and cinnamon sugar pretzels.
20Add melted butter to the pretzel bites.
21Add coarse salt or cinnamon sugar mixture to the pretzel bites.
22Toss the pretzels to incorporate the melted butter and toppings.
23Melt butter in a saucepan over medium heat.
24Whisk in all-purpose flour until well incorporated and free of lumps.
25Slowly pour milk into the saucepan while gently whisking continuously to prevent flour from settling and burning.
26Once the milk mixture thickens, remove the saucepan from the heat.
27Add freshly grated sharp cheddar cheese and all seasonings.
28Gently fold in the cheese until it is melted and smooth.
29In a small bowl, combine all cream cheese frosting ingredients and mix very well with a rubber spatula until smooth.