Brine the beans: Place the beans in a large bowl with the 3 tablespoons of salt and water to cover by several inches. Let sit overnight or for 10 to 12 hours. Drain but do not rinse. Place beans in a large pot with the remaining teaspoon of salt, the onion, thyme, and garlic. Cover with water by several inches. Bring to a boil, then reduce heat so water is gently simmering. Simmer until beans are cooked through, 45 minutes to 1 hour. Let beans cool in their cooking liquid.
Preheat the oven to 425° F. Place 4 cups of the cooked beans in a large strainer or colander. Do not rinse the beans. Let the beans drain as you prepare the salad.
On a rimmed sheetpan, toss the corn kernels with 1 tablespoon olive oil. Season with salt and pepper to taste. Transfer pan to oven and roast for 10 minutes. Remove pan. Let kernels cool briefly.
In a large mixing bowl, place the beans, corn, peppers, onion, scallions, and cilantro. Season with 1 teaspoon kosher salt. Dress with 1/4 cup olive oil and 2 tablespoons vinegar. Toss. Let stand 5 minutes, then toss again, taste, and adjust with more salt, oil and vinegar to taste. I add salt by the 1/2 teaspoon until it tastes right, and I keep a 2-to-1 oil-to-vinegar ratio for the most part—sometimes a splash more vinegar or a squeeze of lime at the end helps.