01 - Dissolve yeast and sugar in warm water in a large bowl. Let stand until foamy, about 5 minutes.
02 - Add flour, salt, and melted butter to the yeast mixture. Mix with a wooden spoon until a shaggy dough forms. Knead for 5-7 minutes until smooth and elastic.
03 - Place dough in a lightly oiled bowl, cover, and let rise in a warm spot until doubled in volume, about 1 hour.
04 - Preheat air fryer to 390°F.
05 - Bring 4 cups water and baking soda to a boil in a medium saucepan.
06 - Punch down dough and turn onto a floured surface. Divide into 6 pieces. Roll each into a ½-inch thick rope and cut into 1-inch pieces.
07 - Working in batches, drop pretzel bites into the boiling baking soda water for 20 seconds. Remove with a slotted spoon and place on a parchment-lined tray.
08 - Brush pretzel bites with beaten egg and sprinkle generously with coarse sea salt.
09 - Arrange bites in a single layer in the air fryer basket. Cook for 6-8 minutes, shaking halfway through, until deep golden brown and crispy. Repeat with remaining bites.
10 - In a small saucepan, melt butter over medium heat. Whisk in flour and cook for 1 minute to form a roux.
11 - Gradually whisk in milk, cooking until slightly thickened, about 2 minutes.
12 - Reduce heat to low. Stir in cheddar, cream cheese, mustard, garlic powder, paprika, and cayenne. Whisk until smooth and creamy. Season with salt and pepper to taste.
13 - Serve pretzel bites warm with zesty cheese dip for dipping.