Thinly slice 10 garlic cloves. Place the whole peeled tomatoes and their juices into a large, deep bowl. Squeeze and crush the tomatoes with your hands until a chunky sauce forms with pieces no bigger than 1 1/2 inch.

Heat 1/2 cup olive oil in a large Dutch oven over medium-low heat until shimmering. Add the garlic and cook for 1 minute. Add 1/4 teaspoon red pepper flakes if desired and cook, stirring occasionally, until the garlic is golden-brown and fragrant, 1 to 2 minutes.

Add 1/4 cup double-concentrated tomato paste. Cook, stirring often, until the paste is darker in color and fragrant, 2 to 3 minutes. Add the tomatoes, 2 fresh basil sprigs, and 1/2 teaspoon kosher salt. Increase the heat to medium-high and bring to a simmer.