Remove the florets of the broccoli and cut them into 1-inch pieces. Place half in a large bowl and half in a small bowl. Cut off the bottom of the stalk and use a vegetable peeler to trim away the woody outer layer. Cut the stalk into 1-inch pieces and place them in the large bowl with the florets.

Heat the oil in a large pot over medium heat. Add the onion and season with salt and pepper. Cook, stirring occasionally, until softened, about 5 minutes. Add potato, large bowl of florets and stalks, chicken stock and chard leaves. Season again with salt and pepper and bring to a boil. Reduce heat, cover and simmer until vegetables are cooked through, about 20 minutes. Meanwhile, cut the remaining florets into 1/4-inch pieces.

Purée the soup using a hand blender or carefully transfer to a blender and purée. Add remaining florets to the puréed soup and cook over medium-low heat until florets are tender, about 10 minutes more. Add cheese, cream, and lemon juice and stir to combine. Taste and add additional salt and pepper if needed.