Bring a large saucepan 3/4 full of salted water to a boil. Add the farro and boil until just tender, 25-30 minutes. Drain and let cool.
Refill the saucepan ¾ full with salted water and bring to a boil. Add the beans and cook until tender-crisp, about 4 minutes. Drain and plunge into cold water to cool. Drain again.
In a large serving bowl, combine the farro, green beans, corn, and scallions. In a small bowl, muddle together the olive oil, minced marjoram, and 1/2 teaspoon salt. Whisk in the vinegar, garlic, and mustard.
Pour the dressing over the salad and toss well. Season with salt and pepper, to taste, then sprinkle with the goat cheese and marjoram leaves and serve.