Add the flour, 88°F filtered water, sea salt, and active sourdough starter to a large mixing bowl. Combine thoroughly until the ingredients come together into a unified, cohesive dough with no significant dry patches remaining.
Begin the stretch-and-fold sequence. Over the following 2 hours, complete four sets of stretch-and-folds, allowing approximately 30 minutes between each set.
During the first set of folds, gently work the thoroughly drained Hatch green chile and 1/4-inch smoked Gouda cubes into the dough. The mixture may initially seem slick or difficult to handle because of the additions, but it should become progressively smoother and stronger with subsequent folds.
After the folding period, leave the dough to ferment at room temperature for up to 8 hours. Allow it to continue until it appears noticeably expanded, puffy, and aerated.
Once bulk fermentation is complete, form the dough into a round loaf. Transfer it upside down, with the seam facing upward, into a banneton or suitable bowl dusted with rice flour.
Cover the shaped dough and place it in the refrigerator overnight. The extended chilled fermentation allows the loaf to proof gradually while further developing its flavor and texture.
When ready to bake, place a Dutch oven inside the oven and preheat to 450°F for a minimum of 30 minutes.
The loaf may be baked directly from refrigeration, or it can rest outside the refrigerator for approximately 1 hour to move closer to room temperature before baking.
Carefully invert the proofed dough onto a sheet of parchment paper. Score the surface as desired so the loaf can expand in a controlled manner during baking.
Wearing suitable oven mitts, carefully remove the fully heated Dutch oven. Lower the scored loaf, together with its parchment paper, into the hot pot.
Carefully pour a few tablespoons of water between the parchment paper and the sides of the Dutch oven. The water will boil immediately upon contacting the heated surface, so use appropriate caution.
Place the lid on the Dutch oven and bake the loaf at 450°F for 20 minutes.
Remove the lid and continue baking for an additional 30 minutes, or until the crust develops a deep golden-brown color and the loaf produces a hollow sound when tapped.
Remove the baked sourdough from the Dutch oven and place it on a wire cooling rack. Allow it to rest for at least 1 hour before slicing so the interior crumb can set properly.