In a large mixing bowl, whisk together the active sourdough starter and water until mostly dissolved.
Add the bread flour and mix with a spoon or spatula until no dry spots remain and a shaggy dough forms.
Cover the bowl and let the dough rest (autolyse) for 30 minutes at room temperature.
Sprinkle the salt and olive oil over the dough and pinch and fold until fully incorporated.
Add the dried oregano, basil, thyme, rosemary, and minced garlic (or garlic powder) and gently knead or fold to distribute evenly.
Cover the bowl and begin bulk fermentation at room temperature (about 21–24°C), letting the dough rise for 3–4 hours.
During the first 1.5 hours of bulk fermentation, perform 3–4 sets of stretch-and-folds every 30 minutes, lifting and folding each side of the dough toward the center.
After the last set of folds, gently sprinkle the mozzarella and Parmesan over the dough and perform a few gentle folds to incorporate the cheese without tearing the gluten too much.
Allow the dough to finish bulk fermenting until it has risen by about 50% and looks airy with small bubbles along the sides.
Lightly flour the work surface and gently turn the dough out, taking care not to deflate it completely.
Pre-shape the dough into a loose round by folding the edges toward the center and flipping it seam-side down, then let it rest uncovered for 15–20 minutes.
Final-shape the dough into a tight round or oval loaf by gently stretching and tucking to build surface tension, keeping most of the gas inside.
Dust the banneton or towel-lined bowl with semolina flour or cornmeal and a little bread flour to prevent sticking.
Place the shaped dough seam-side up into the prepared banneton or bowl.
Cover and refrigerate the dough for 8–12 hours for a cold retard and deeper flavor development.
About 45 minutes before baking, place the Dutch oven and its lid into the oven and preheat to 250°C (480°F).
When ready to bake, carefully remove the hot Dutch oven from the oven and remove the lid.
Turn the chilled dough out from the banneton onto a piece of parchment paper so it is seam-side down.
Score the top of the loaf with a sharp lame or serrated knife in one long slash or a pattern of your choice to control the expansion.
Using the parchment as a sling, carefully lower the dough into the hot Dutch oven and cover with the lid.
Bake covered at 250°C (480°F) for 20 minutes to create steam and oven spring.
After 20 minutes, remove the lid, reduce the temperature to 220°C (430°F), and bake for another 15–20 minutes until deep golden brown and the internal temperature reaches about 96°C (205°F).
Carefully remove the loaf from the Dutch oven and place it on a wire rack to cool completely for at least 1 hour before slicing.
Slice with a serrated knife and serve plain, toasted, or alongside soups, salads, or pasta dishes.