Preheat the oven to 400°F. Slice the top off the head of garlic to expose the cloves. Drizzle with olive oil and sprinkle with a pinch of salt. Wrap in foil and roast for 35 to 45 minutes, or until the cloves are soft and golden. Let cool, then squeeze the cloves out of the skins.
In a large bowl, mix the active sourdough starter and warm water until mostly combined. Add the flour and salt, then mix until a shaggy dough forms. Cover and let the dough rest for 30 minutes.
Add the cooled roasted garlic and chopped rosemary to the dough. Gently fold them in during the first set of stretch and folds.
Complete 3 to 4 sets of stretch and folds, spaced about 30 minutes apart. Keep the dough covered between each set.
Let the dough bulk ferment at room temperature until it looks puffy, has visible bubbles, and has risen about 50 to 75 percent. This may take several hours depending on the warmth of your kitchen and the strength of your starter.
Turn the dough out onto a lightly floured surface. Shape it into a round loaf, building tension on the outside of the dough.
Place the shaped dough seam side up in a floured banneton or a bowl lined with a floured tea towel. Cover and refrigerate for at least 1 hour or up to 48 hours.
When ready to bake, place a Dutch oven in the oven and preheat to 450°F.
Turn the chilled dough out onto parchment paper. Dust with flour if desired, then score the top with a sharp lame or knife.
Carefully place the dough into the hot Dutch oven. Cover and bake for 30 minutes. Remove the lid and bake for another 15 to 25 minutes, or until the crust is deep golden brown and crisp.
Transfer the bread to a wire rack and let it cool completely before slicing.