Combine 2 cups flour, sugar, undissolved yeast, and salt in a large bowl. Heat milk, water, and oil until very warm (120° to 130°F); stir into flour mixture.
Stir in enough remaining flour to make soft dough. Knead on floured surface until smooth and elastic, about 4 to 6 minutes. Cover; let rest on floured surface 10 minutes.
Divide into 6 equal pieces. Roll each piece into a 16-inch rope. Cover; let rest for 5 to 10 minutes until risen slightly.
Preheat oven to 425°F. Line 2 baking sheets with parchment paper.
Use a knife, kitchen scissors, or pizza cutter to cut each dough rope into 1-inch pieces to create pretzel bites.
Arrange pretzel bites on prepared baking sheets and make sure none of the pretzel bites are touching. Brush with beaten egg.
Bake in preheated oven for 12-15 minutes, or until golden brown.
Meanwhile, mix together the sugar and cinnamon in a medium bowl.
Remove from oven and allow the pretzel bites to cool for about 5 minutes, or until they are cool enough to be handled.
Dip pretzel bites into melted butter and then roll in the cinnamon sugar mixture until they are fully coated.
In a large bowl with an electric mixer, beat cream cheese for about 2 minutes. Add in powdered sugar and beat until smooth and creamy. Scrape down the sides and bottom of the bowl with a spatula and continue beating for an additional 2 minutes. Add in vanilla extract and mix until combined. Gradually add in milk, 1 teaspoon at a time until optimal dipping texture is achieved.
Serve pretzel bites warm with cream cheese icing.
Notes
If you prefer salted pretzels, simply add coarse salt to the tops of each pretzel bite after you brush the bites with the egg wash. Serve with mustard, pub cheese, marinara or your favorite dipping sauce.
These pretzel bites are best served warm. If necessary, you can reheat them in the microwave for about 15 seconds before serving.