Place beans, soaking liquid, and 1 teaspoon salt in a large pot. Liquid should cover by 2 inches; adjust as necessary. Bring to a boil. Reduce heat; simmer gently. Cook, stirring occasionally, until beans are tender, about 1 hour. Drain, and transfer to a bowl. (Makes 5 cups beans.)
Heat a large, heavy skillet over medium-high heat, and add corn. Cook, stirring occasionally, until corn begins to brown, 4 to 5 minutes. Add garlic, and cook, stirring frequently, until corn is browned and begins to pop, 3 to 4 minutes. Add to beans. Wipe skillet, return to medium-high heat, and add 1 teaspoon oil. Add tomatoes, in a single layer, and thyme. Cook, turning occasionally, until soft and beginning to char, 6 to 7 minutes.
Coarsely chop tomatoes, and add to beans. Whisk vinegar, red-pepper flakes, and remaining 1/2 teaspoon salt and 2 tablespoons oil in a small bowl. Pour over beans, stirring gently. Spoon over lettuce, and top with cheese.