Place tomatoes, vinegar, brown sugar, salt, pepper, and thyme in non-reactive pot. Bring to boil. Reduce to low. Simmer 30 minutes or until most liquid is evaporated. Puree with immersion blender. Adjust seasoning. Cool.
To assemble the sandwich, spread 1 ounce of goat cheese on each slice of bread. Spread jam in thick layer to ¼-inch from crust. Fold halves together. Butter outside of each side of sandwich. Heat non-sick skillet on medium-high heat. Cook sandwich 3-5 minutes per side until bread is golden brown.