Arrange potatoes in a microwave-safe dish; cover tightly with plastic wrap. Cut a 1/2-inch slit in plastic. Microwave at HIGH 8 minutes or until tender; transfer to a bowl. Microwave buttermilk in a microwave-safe cup 30 seconds; pour buttermilk and 2 tablespoons olive oil over potatoes. Mash until mostly smooth.
While potatoes cook, heat 2 teaspoons olive oil in a large skillet over medium-high heat. Add broccoli florets to pan; cook 2 minutes, stirring frequently. Add lemon juice and water to pan; cover, reduce heat, and cook 4 minutes or until tender. Stir broccoli, cheese, salt, and pepper into potatoes. Serve potatoes immediately.