To roast the garlic:
Cut top off head of garlic to expose the cloves. Place in a ceramic baking dish. Drizzle 1 tbsp. olive oil on head of garlic.
Bake at 400º until soft and aromatic and a light caramel color on top has developed, about 40-50 minutes. Let cool.
Squeeze head from the base to push out roasted garlic cloves into a small mixing bowl. Mash with a fork to form a paste. Season to taste with salt. Use immediately or refrigerate for up to 4 days.
To make the dough:
Sprinkle yeast on top of water in the bowl of a stand mixer and stir gently until dissolved. Allow to proof until slightly foamy and aromatic to ensure yeast is alive, about 5 minutes. Add oil, 1/2 of flour and salt. Mix on medium low speed with a dough hook until incorporated, scraping down sides as necessary. Add remaining flour and kneed on low until the dough is smooth and elastic, about 5 minutes. Turn out onto a floured surface, kneed a few turns by hand and shape into a ball. Place dough in a bowl and cover with a plastic wrap on top of bowl not touching the dough. Let dough rise at room temperature until doubled, about 60-75 minutes, or in the refrigerator overnight.
To make the focaccia:
Rub a baking sheet, including sides, generously with some of the olive oil. Punch dough down gently to deflate. Shape onto baking sheet using fingertips until dough is about 1/4" thick. Spread with roasted garlic, oil and course sea salt. Dimple dough with fingers and cover with plastic wrap not touching the dough. Let rise 20-30 minutes at room temperature. Bake at 400º until light golden brown, about 25 minutes. Cut and serve immediately.