Combine water, sugar, and salt in the bowl of a stand mixer and sprinkle yeast on top. Let sit for 5 minutes until foamy.

Add flour and melted butter. Use the dough hook to mix on low speed until combined, then increase to medium and knead until smooth (approx. 5 minutes).

Place dough in a greased bowl, cover with plastic wrap, and let rise in a warm place for 1 hour or until doubled in size.

Preheat oven to 450°F (230°C). Bring 10 cups of water and baking soda to a rolling boil.

Divide dough into 8 equal pieces. Roll each into a long rope, flatten slightly, place cheddar sticks in the center, and pinch dough around cheese to seal.

Twist the stuffed ropes into a pretzel shape. Dip each pretzel into the boiling water for 30 seconds.

Place on parchment-lined sheets. Brush with egg wash, sprinkle with rosemary and sea salt.

Bake for 12-15 minutes until dark golden brown. Serve warm while the cheese is gooey.