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 yeast mixture. Mix with wooden spoon until shaggy dough forms, then 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 size, approximately 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 transfer to floured surface. Divide into 6 pieces, roll each into ½-inch thick rope, and cut into 1-inch pieces.
07 - Working in batches, drop bites into boiling baking soda water for 20 seconds. Remove with slotted spoon and place on parchment-lined tray.
08 - Brush pretzel bites with beaten egg and sprinkle generously with coarse sea salt.
09 - Arrange bites in single layer in air fryer basket. Cook for 6–8 minutes, shaking basket halfway through, until deep golden brown and crispy. Repeat with remaining bites.
10 - Melt butter in small saucepan over medium heat. Whisk in flour and cook for 1 minute to form roux.
11 - Gradually whisk in milk, stirring constantly until slightly thickened, about 2 minutes.
12 - Reduce heat to low. Stir in cheddar, cream cheese, mustard, garlic powder, paprika, and cayenne. Whisk until completely smooth. Season with salt and pepper to taste.
13 - Serve pretzel bites immediately with warm zesty cheese dip for dipping.