Feed your starter 6–12 hours before mixing your dough. It should be bubbly and active by the time you’re ready to bake.
Preheat your oven to 425°F. Place the garlic cloves (peels still on) on a small piece of aluminum foil, drizzle with olive oil, and loosely wrap them up—leaving a little room for air to circulate. Roast for about 30 minutes, until golden, soft, and fragrant. Let cool slightly, then squeeze the garlic from the peels, mash, and mix with the chopped sun-dried tomatoes. Set aside.
In a large bowl, whisk together warm water and sourdough starter until mostly dissolved. Add the bread flour and salt. Mix until no dry bits remain and you have a shaggy dough. Cover and let rest for 20 minutes.
Lightly dampen your hands. Gently press the dough into a flat-ish shape in the bowl. Sprinkle on ¼ of the garlic-tomato mixture and ¼ of the parmesan cheese. Do a stretch and fold (lift, stretch, and fold the dough over itself), rotate the bowl 90°, and repeat. Continue until all the garlic, tomatoes, and cheese are added. Shape the dough into a loose ball and place seam side down in the bowl. Cover and rest for 20 minutes. Do 3 more rounds of stretch and folds, each spaced 20 minutes apart.
Cover the dough and let it rise at room temperature until it's puffy, jiggly, and nearly doubled in size. This usually takes 4–12 hours (or longer), depending on room temp and your starter. Use a straight-sided container to track the rise more easily.
Lightly flour your counter and gently turn the dough out. Pull it into a rough rectangle. Fold the long edges toward the center (like a letter), then fold the short sides. Flip seam-side down, gently round it into a ball. Cover and let rest for 15 minutes.
For a round loaf (boule), repeat the shaping technique above. For an oval loaf (batard), fold the short edges in, then roll into a tight log from the long edge, pinching the ends to seal.
Generously flour your proofing basket with rice flour. Place the dough seam-side up in the basket. Pinch or stitch the seam if needed. Cover and refrigerate overnight for 12–16 hours.
Place a lidded Dutch oven inside your oven and preheat to 450℉. Let the Dutch oven heat for an extra 30-60 minutes once the oven reaches temperature.
Turn the dough out onto a bread sling or piece of parchment paper. Score the top as desired with a lame or sharp knife. Carefully place 2 ice cubes in the Dutch oven for steam. Use the sling or parchment paper to transfer the dough into the hot Dutch oven. Cover immediately with the lid to trap the steam inside.
Bake at 450℉ for 40 minutes with the lid on. Then, remove the lid and bake for an additional 5-10 minutes, if needed, to achieve your desired crust color.
Transfer the loaf to a wire rack and let it cool for at least 2–4 hours before slicing.