In a stand mixer bowl (or large mixing bowl), stir together warm water, brown sugar, and yeast. Let bloom for 5 minutes until frothy and aromatic.

Add melted butter, fine salt, and bread flour. Knead on medium-low speed for 5 minutes (or 8 minutes by hand) until smooth, elastic, and slightly tacky. Cover bowl and let rest for 15 minutes.

Preheat oven to 425°F (220°C) and line two large baking sheets with parchment paper. Bring 6 cups of water and 1/3 cup baking soda to a gentle rolling boil in a wide saucepan.

Divide dough into 4 equal portions. Roll each piece into a 3/4-inch thick rope, then cut into 1-inch bite-sized pieces using a bench scraper or sharp knife.

Drop pretzel bites into the boiling soda bath in batches of 12 to 15. Boil for exactly 20 to 25 seconds, then remove with a slotted spider strainer, draining excess liquid, and transfer to prepared baking sheets.

Bake at 425°F for 12 to 14 minutes until deeply golden brown and puffed. Remove from oven and immediately brush generously with melted garlic butter and sprinkle with coarse pretzel salt.

While pretzel bites bake, melt butter in a medium saucepan over medium heat. Whisk in flour and cook for 1 minute until fragrant. Gradually whisk in warm milk and heavy cream, simmering for 2 to 3 minutes until thickened.

Remove pan from heat and whisk in Dijon mustard, smoked paprika, garlic powder, and freshly shredded cheddar cheese in batches until completely smooth, glossy, and silky. Serve immediately alongside warm pretzel bites!