Mix the sourdough starter with the water until mostly dissolved. Add the bread flour and mix until no dry flour remains. Cover and rest for 30 minutes.
Add the salt and work it into the dough using damp hands with pinching and folding motions.
Begin bulk fermentation. Perform 3–4 stretch-and-fold sessions every 30 minutes over the next 2 hours.
During the second or third fold, gently incorporate the shredded cheddar cheese into the dough.
Continue bulk fermentation until the dough becomes airy and increases in volume by about 50%.
Turn the dough onto a lightly floured surface, shape into a loose round, and rest for 20 minutes.
Shape into a tight boule and place seam-side up in a floured proofing basket.
Proof at room temperature for 1–2 hours or refrigerate overnight.
Preheat a Dutch oven to 475°F (245°C) for at least 30–45 minutes.
Turn the dough onto parchment paper, score the top, sprinkle with extra cheddar, and arrange the jalapeño slices.
Bake covered for 20 minutes.
Remove the lid and bake another 18–22 minutes until deeply golden brown.
Cool on a wire rack for at least 1 hour before slicing.