To make the bacon and tomato jam, heat the tomatoes, bacon, salt, pepper, garlic, vinegar, and sugar over medium-high heat until they bubble up. Reduce the heat and cook the jam over medium-low heat for about 30 minutes, until thick.
Next, make the sammies: Butter one side of sliced bread and build the sandwiches with the buttered sides facing out. Spread the sandwiches with jam on one side and stack up the bacon, tomatoes, chives or shallots and cheese and set the top slice of bread into place.
Heat a skillet over medium heat and cover the sandwich with foil. Cook to deep golden, 7-8 minutes, turning occasionally and pressing the sandwich as it cooks. Repeat with the remaining sandwiches.