Roast garlic: Preheat oven to 400°F (200°C). Trim top of garlic head, drizzle with a little olive oil, wrap in foil and roast 30–40 minutes until soft. Cool and mash 6–8 cloves into a paste.
Combine dry: In a large bowl, whisk together flour and salt. If using active dry yeast, proof it in 60 g water first; if instant, mix directly into the flour.
Mix dough: Add yeast (or foamy yeast mixture), remaining lukewarm water (≈290 g), 40 g olive oil, grated Parmesan (reserve ~20 g for topping), and roasted garlic paste (start with 2 tbsp). Stir until a sticky, shaggy dough forms.
Bulk rise: Cover and let rest at room temperature (about 1–2 hours) until puffy and roughly doubled. For best flavor, refrigerate for 12–24 hours (cold ferment) and bring to room temp before shaping.
Prepare pan: Generously oil a 9×13-inch pan with about 1–2 tbsp of the reserved oil. Gently transfer the dough into the pan. With oiled fingers, coax the dough to the edges — it may resist; let it rest 10 minutes and continue.
Dimple and top: Use fingertips to press deep dimples across the dough. Drizzle remaining olive oil over the top so it pools in dimples. Dot additional roasted garlic in several places, sprinkle reserved Parmesan and rosemary, and finish with flaky sea salt.
Final proof: Cover and let proof 30–60 minutes at room temperature until puffy and nearly doubled.
Bake: Preheat oven to 450°F (230°C). Bake focaccia 18–25 minutes until deep golden brown and crisp on top. (Optional: broil 30–90 seconds at the end for extra color — watch closely.)
Finish: Remove from oven, brush lightly with a little extra olive oil, sprinkle extra Parmesan or flaky salt if desired. Cool 10 minutes in pan, then transfer to a wire rack. Slice and serve warm or at room temperature.