01 - Whisk together all-purpose flour, instant yeast, granulated sugar, and salt in a large mixing bowl.
02 - Add cream soda and melted unsalted butter to the bowl, then mix until a shaggy dough forms.
03 - Transfer dough to a lightly floured countertop and knead for 5 to 7 minutes until smooth and elastic.
04 - Place the dough in a greased bowl, cover, and let rise at room temperature for approximately 45 minutes, until doubled in volume.
05 - Preheat oven to 400°F. Line a large baking sheet with parchment paper.
06 - Punch down the risen dough and divide evenly into 24 pieces.
07 - Flatten each dough piece into a rectangle, fill the center with a mound of shredded sharp cheddar cheese, then roll tightly into a stick, pinching to seal the edges.
08 - Bring water to a boil in a saucepan, then carefully add baking soda.
09 - Place each stick into the boiling baking soda solution for 20 seconds, then remove with a slotted spoon and transfer to the prepared baking sheet.
10 - Brush each stick with beaten egg using a pastry brush and sprinkle with coarse sea salt.
11 - Bake for 16 to 18 minutes, or until sticks are deep golden brown and crisp.
12 - Allow biscuit sticks to cool slightly before serving.