1. Combine boiling water and tomatoes in a bowl; cover and let stand 30 minutes or until soft. Drain and finely chop.
2. Heat 1 tsp oil in a large nonstick skillet over medium heat. Add 1/3 cup shallots, sugar, and garlic; cook 4 minutes or until lightly browned, stirring frequently. Spoon into a bowl; stir in 1-1/2 tsp vinegar.
3. Combine chopped tomatoes, shallot mixture, cheese, basil, and 1/4 tsp salt, stirring well.
4. Cut a horizontal slit through thickest portion of each chicken breast half to form a pocket.
5. Stuff about 2 Tbsp cheese mixture into each pocket. Sprinkle chicken evenly with 1/2 tsp salt and black pepper.
6. Heat 1tsp oil in pan over medium-high heat. Add chicken; cook 6 minutes on each side or until done.
7. Remove chicken from pan; cover and keep warm.
8. Add broth, remaining shallots, 2 Tbsp vinegar, and thyme; bring to a boil.
9. Combine cornstarch and water, stirring with a whisk. Add cornstarch mixture to pan; bring to a boil. Cook 1 minute or until sauce is slightly thick, stirring constantly.
10. Serve sauce over chicken.