1 tablespoon olive oil, divided
1 1/2 cups chopped leeks (about 2 small stalks; white and pale green parts only)
1 8-ounce container sliced crimini (baby bella) mushrooms
2 garlic cloves, pressed
2 1/4 teaspoons minced fresh rosemary
1 14.5-ounce can diced tomatoes in juice
1 cup pearl barley
4 cups (or more) vegetable broth
1 bunch kale (about 8 ounces), trimmed, center stalks removed, leaves coarsely chopped (about 8 cups packed)