Place the wheat berries and 1 teaspoon salt in a medium saucepan. Add 5 cups of water and bring to a boil, then cover and reduce to a simmer. Cook, undisturbed, for 1 1/2 hours. Uncover and continue to cook until the water has evaporated and the wheat berries are softened with just a little bite to them, about 30 minutes more. Stir in the butter and a good amount of black pepper and set aside.
Meanwhile, bring a medium pot of heavily salted water to a boil. Fill a medium bowl with ice water. Add the beans to the boiling water and cook until crisp-tender and bright green, 4 to 5 minutes. Use a slotted spoon to remove them from the hot water and immediately submerge them in the ice water to stop the cooking. Drain and set aside.
Combine the honey, sherry vinegar, zest of 1 lime, juice of all the limes, 1 teaspoon salt and a good amount of black pepper in a small bowl. Slowly drizzle in the olive oil, whisking constantly, until emulsified. Add the tomatoes, garlic, jalapeno, onion, green beans, 1 teaspoon salt and a few grinds of black pepper and toss until well combined. Set aside for at least 30 minutes, or until the wheat berries are done cooking. Fold the basil and mint into the bowl.
Spoon the wheat berries into the bottom of a serving bowl or platter, then use a slotted spoon to spoon the tomato mixture over the top. Sprinkle with a little more salt and serve with the juices left in the bowl, if desired.