How to Make It
In a standing mixer fitted with the dough hook, combine the flour, yeast and salt with the 3 tablespoons of olive oil and 2 1⁄2 cups of cold water. Mix at low speed until the flour is evenly moistened. Beat at medium speed until the dough is smooth and glossy, about 3 minutes longer; the dough will be soft and somewhat sticky. Transfer the dough to an oiled baking sheet, cover with a bowl and let rest for 20 minutes.
With lightly floured hands, press the dough into an 8-inch square and fold it in thirds. Rotate the baking sheet and fold the dough in thirds again. Cover the dough with the bowl and let rest for 20 minutes. Repeat the folding and resting twice more.
Divide the dough in half and place each piece in a lightly oiled bowl. Cover with plastic wrap and refrigerate overnight.
Preheat the oven to 300°. On a baking sheet lined with parchment paper, arrange the tomatoes cut side up and season them with kosher salt and black pepper. Roast for about 1 hour, until the tomatoes are slightly dry but soft.
Meanwhile, in a small ovenproof saucepan, combine the olive oil, garlic, rosemary, crushed red pepper and lemon zest and bring to a simmer over moderate heat. Cover, transfer to the oven and cook until the garlic is tender and lightly golden, about 35 minutes. Discard the lemon zest; let the garlic cool in the oil.
Bring the dough to room temperature. Generously oil 2 baking sheets. Stretch each piece of dough into an 11-by-14-inch rectangle on a baking sheet and let rest for 30 minutes.
Increase the oven temperature to 475°. Arrange the tomatoes cut side up on the dough and drizzle with some of the garlic oil. Dot the focaccia with the garlic confit. Bake the focaccia in the upper and lower thirds of the oven until golden and crusty, about 20 minutes, shifting the pans from top to bottom and front to back halfway through baking. Sprinkle with sea salt, cheese and basil, drizzle with some of the garlic oil and serve.