Hull the tomatoes, then rough chop and transfer them to a bowl along with any of the juices that accumulate on the cutting board; set aside.

In a medium-sized skillet, warm the oil over medium heat.

Add the shallot and garlic and cook, stirring constantly, until softened, for 1 ½ to 2 minutes.

Add the tomatoes and any juices, the sugar, vinegar and a generous pinch of salt, stir to combine and bring to a boil.

Reduce to a simmer and cook, stirring often and using the back of a wooden spoon to break up the tomatoes, until jammy, about 40 minutes. As the jam thickens, you may need to stir it more frequently.

Season with additional salt, as needed.

Transfer to a heat-resistant container and cool completely.