Preheat your oven to 300°F and place a rack in the middle. Grab a small baking dish or an oven-safe bowl and pour olive oil into it. Add the halved garlic with the cut sides down. Cover tightly with foil and place it in the oven. Bake until the garlic is tender and golden, which should take about 45 minutes to 1 hour.
Once the garlic is roasted, carefully pour the roasted garlic oil through a mesh strainer into a clean bowl. Set aside the garlic cloves and discard any solids. Allow the roasted garlic oil to cool completely before using it in the next steps.
Rinse the bowl of your stand mixer with warm water to preheat it slightly. Dry the bowl, then add the yeast. Cover it with 1 ¾ cups of warm water, gently stirring to dissolve. Let it sit for 3 to 5 minutes until it becomes frothy.
Using the dough hook, start the mixer on low speed. Gradually add the flour, salt, and 2 tablespoons of the roasted garlic oil. Increase the speed to medium once the dough starts to combine. Make sure to stop occasionally to scrape down the sides and ensure everything is mixed well. Continue mixing until the dough is smooth and slightly sticky, which should take around 8 to 10 minutes.
Coat a large bowl with 2 teaspoons of the roasted garlic oil. Add the ball of dough into the bowl, turning it to coat all sides with oil. Cover the bowl with a kitchen towel, and place it in a warm spot to let it rise until doubled in size for about 1 hour 45 minutes.
After the dough has risen, prepare a rimmed baking sheet by adding 1 teaspoon of the roasted garlic oil, spreading it evenly over the bottom and sides. Punch down the dough gently to release any air bubbles and transfer it to the baking sheet. Carefully stretch the dough out to the edges of the pan. Cover it again with a tea towel, allowing it to rest in a warm spot for about 30 minutes.
While the dough is resting, preheat your oven to 450°F. Once the resting time is up, uncover the dough and dimple the surface with your oiled fingertips, creating little pockets.
Brush more of the roasted garlic oil on top of the dough, then dot it with the reserved roasted garlic cloves. Sprinkle generously with fresh rosemary and a pinch of flaky sea salt for a savory finish.
Place the baking sheet into the oven and immediately reduce the temperature to 375°F. Bake the focaccia until it’s golden brown, which should take about 20 to 25 minutes. Keep an eye on it to prevent over-browning.
Once baked, transfer the focaccia to a wire rack to cool slightly before slicing. Enjoy the Roasted Garlic Focaccia warm, drizzled with even more olive oil or served with your favorite dip!