1. Rinse beans, removing debris; transfer to a large bowl. Add cold water until covered by at least 2 inches. Refrigerate overnight.

2. Drain; transfer beans to a large pot and add enough water to cover by 4 inches. Add yellow onion, carrot, and celery; bring to a simmer. Season generously with salt; reduce heat to medium-low and continue simmering until beans are tender but not falling apart, 40 to 50 minutes. Drain; transfer to a large bowl. Remove and discard vegetables. (Or, if not using immediately, let cool in liquid and refrigerate up to 5 days.)

3. Place chiles over the flame of a gas burner or on a grill; roast, turning, until charred on all sides, about 10 minutes. Transfer to a bowl and cover with a plate; let cool slightly. When cool enough to handle, use a paring knife to remove charred skins. Remove stems and seeds; cut chiles into 1/2-inch pieces.

4. In a small bowl, whisk together vinegar and oil. Drizzle over beans; add roasted chiles, red onion, cilantro, and tomatoes. Gently toss to coat. Season with salt and pepper, sprinkle with cheese, and serve.