Combine the active starter, water, egg, oil, salt, and about a cup and a half of the flour in a stand mixer. Beat on low speed until smooth.
Add enough additional flour to make a soft dough. Mix for 5-10 minutes or until stretchy. (You should be able to pull the dough apart until it is so thin you can almost see through it.)
Add the cheddar and jalapeño peppers. Pulse a few times, then dump out onto a counter. Knead a few times until the cheese and peppers are evenly distributed.
Transfer the dough to a large bowl sprayed with cooking spray. Cover the bowl with a lid or plastic wrap and place in the refrigerator overnight (12-18 hours).
The next day, spray your counter with cooking spray. Dump out the dough and form it into a tight ball, pressing out any air bubbles.
Place the dough ball on a piece of parchment paper and transfer to a 4-quart Dutch oven. Cover and let rise for 6-8 hours in a warm place until doubled.
Preheat your oven to 425°. Cut slits on top of the dough with a bread lam or razor blade . If desired, sprinkle a little bit of grated cheddar on top.
Bake the bread covered at 425° for 40-45 minutes. Remove the lid and bake for another 10-20 minutes or until the crust is browned and the internal temperature is at least 195°.
Carefully remove the loaf to a wire rack. Remove the parchment paper and let cool completely.