Remove stems from kale. Wash and pat dry; coarsely chop to measure 9 cups.
Bring water to a boil in a Dutch oven. Add potato; cook 5 minutes or until almost tender. Add kale; cook 2 minutes or until vegetables are tender. Drain potato mixture in a colander over a bowl, reserving 1/2 cup cooking liquid.
Heat 1 tablespoon oil in a large skillet over medium heat. Add red pepper and garlic; sauté 30 seconds. Add potato mixture, reserved 1/2 cup cooking liquid, tomato, lemon juice, salt, and black pepper; stir gently. Cook 5 minutes or until thoroughly heated, stirring occasionally. Spoon 1 1/2 cups potato mixture onto each of 4 plates. Drizzle each serving with 1/2 teaspoon oil. Arrange 1 tablespoon cheese over each serving.