Combine 1 cup boiling water and sun-dried tomatoes in a small bowl; let stand 15 minutes. Drain.
While tomatoes hydrate, heat oil in a large nonstick skillet over medium-high heat. Add onion, bell pepper, and garlic. Cook 6 minutes or until vegetables are tender, stirring frequently. Stir in sun-dried tomatoes, brown sugar, and next 7 ingredients. Bring to a boil; reduce heat to medium-low, and simmer, uncovered, 6 minutes or until slightly thick, stirring occasionally.
Stir meatless crumbles into vegetable mixture; cook over medium-high heat 4 minutes or until thoroughly heated, stirring frequently.
Spoon about 1/2 cup vegetable mixture onto each bun bottom; cover with bun tops.