Place flour in a large bowl and make a well in the center.

Add 2 tablespoons olive oil, salt and 1¼ cups water, and stir until a dough forms. Transfer to a floured work surface and knead until smooth and elastic, about 6-8 minutes. Transfer dough to a lightly oiled bowl, cover with plastic wrap, and let rest at room temperature for 30 minutes.

Meanwhile, heat remaining 2 tablespoons oil in saucepan. Add garlic and cook, stirring, until fragrant, about 1 minute. Add tomatoes, season with salt and pepper and cook until thickened and reduced a bit, about 10 min. Add basil. Set aside to cool.

Transfer dough to a floured work surface, and using a rolling pin, roll dough into a thin, 1/16th inch rectangle. Arrange dough so that long edge is parallel to edge of counter.

Spread 1 cup tomato sauce over dough in a thin layer and sprinkle with 1 ½ cups grated cheese; season with salt and pepper. Fold left third of dough toward center, spread top with ¼ cup sauce and sprinkle with 5 tablespoons cheese; season with salt and pepper. Fold right third over center to meet left edge, and repeat with sauce, cheese, and salt and pepper. Fold in top and bottom so they meet in center; spread top with remaining sauce and cheese; season with salt and pepper. Fold top half over bottom half, like closing a book, and transfer to a baking sheet lined with parchment paper.

Bake for 10 minutes. Reduce oven temperature to 400 degrees and continue baking until dough is set and slightly charred, about 60-65 minutes. Let cool for 10 minutes before slicing into squares.