To make the tomato jam, add all ingredients for the jam to a medium saucepan. Bring to a boil, stirring often.
Once boiling, reduce to a simmer. Cook until the mixture is thickened to jam consistency, about 1 hour 15 minutes. Stir occasionally to make sure nothing sticks to the bottom. Season with salt to taste. Transfer to an airtight container and cool in the refrigerator until ready to use.
To make the grilled cheese, cut the baguette into two 7-inch pieces. Slice the pieces in half horizontally. Butter the sliced sides with 1 Tbsp each. Heat a large skillet over medium heat.
Spread 1 to 2 Tbsp of the tomato jam on the crusty side of two pieces of bread each. I like to start with the bottom piece that has the flatter outside to begin with. Stack cheese on the top of the crusty side of the bread.
Top with the other half of the bread. Cook the grilled cheese as normal. I like to weigh mine down with another pan to form a sort of press as it cooks. It'll take about 2 to 3 minutes per side, or until the cheese is melted and the outside of the bread is golden brown.
Serve immediately with a side of tomato soup, if desired.