In a small bowl, stir the brown sugar into the warm water to dissolve, then quickly stir in the active dry yeast. Set aside for 5-10 minutes, until foamy.
Stir the extra virgin olive oil into the bowl. Using a wooden spoon, mix in the flour one cup at a time. Transfer the dough onto a clean surface to knead together for 5 minutes, until smooth.
Transfer the dough into a lightly greased bowl and cover with a damp tea towel or saran wrap. Allow the dough to rise for 45 minutes to 1 hour, until doubled in size.
Preheat oven to 450F.
Punch down the dough and knead lightly for 15 seconds. Roll the dough out to a rectangular-shape that's 1/2" thick, then cut the dough into 12 equal-sized strips. In each strip, add a strip of cheese into the center. Pinch together the dough around the cheese and use your hands to shape the dough into a pretzel stick-like shape.
Place the cheese-stuffed dough sticks on a pan lined with parchment paper. Allow them to sit out uncovered for 25 minutes.
Bring a large pot of water to a boil over medium heat, then stir in the baking soda. Using two slotted spoons, transfer each stick into the water to sit for 18-20 seconds on each side. Then, transfer each back to the parchment-lined pan.
Brush with an egg wash or olive oil. Garnish with Maldon Sea Salt or sesame seeds. Bake for 10 minutes, or until golden brown.