Slice the tomatoes in half and scoop out the seeds. Set a box grater over a large bowl and press the cut side of the tomato flesh against the large holes of the grater. Grate the tomato flesh into the bowl, leaving the skins behind.

Heat the olive oil in a medium pot over low heat. Add the shallot, garlic, salt, and a few grinds of pepper and cook for 3 minutes, stirring often.

Add the tomatoes, tomato paste, balsamic vinegar, cane sugar, oregano, red pepper flakes, and basil sprig. Cover and simmer over low heat for 30 minutes, stirring occasionally. Remove and discard the basil sprig and season to taste.