Pour tomatoes into a large bowl and crush with a potato masher or with your hands. Pour 1 cup water into tomato can and slosh it around so that you get all the juices left behind. Reserve.
Heat the olive oil in a large skillet over medium heat. When hot, add the sliced garlic.
When the garlic begins to sizzle (make sure not to brown), pour in the tomatoes and reserved water. Stir in the grated carrot, red pepper flakes, oregano and sea salt.
Place the sprig of basil (stem and all) on top of the sauce. Allow it to wilt and submerge into the sauce. Simmer until the sauce has thickened some, about 15 minutes. Check the seasonings, adjust if necessary, then serve or let cool, place into an airtight container and place into fridge until using.