Bring a large stockpot of water to boiling. Add trimmed beans; boil until crisp-tender, about 8 minutes. Drain well in a colander.
Meanwhile, cut basil leaves into thin strips (chiffonade). Melt butter in very large skillet over medium-high heat. Add beans; cook until beginning to brown, 8 to 10 minutes. Add halved cherry tomatoes, salt and pepper; cook until tomatoes begin to soften, about 3 minutes. Stir in vinegar. Remove skillet from heat. Stir in basil. Serve immediately, or cool to room temperature.