Prepare the tomato jam by sautéing the onion in olive oil until translucent. Add tomatoes, sugar, salt, pepper, and balsamic vinegar; simmer for 15-20 minutes until thickened.

While the jam cooks, slice the bread into small squares or triangles.

Assemble the sandwiches by spreading butter on one side of each bread piece. Layer cheese on top and spoon some tomato jam onto another piece before pressing them together.

Grill the sandwiches in a non-stick skillet over medium heat for about 3 minutes per side until golden brown.

Slice diagonally and serve immediately with extra tomato jam for dipping if desired.