Add olive oil to a large cooking pot over medium heat. When oil is hot, add leeks and garlic. Sauté for a couple of minutes to soften, stirring often to keep the garlic from burning.
Add the potato, broccoli and stock. Stir and mix in the sea salt. Cover and let simmer for 15-20 minutes or until the potatoes and broccoli are fork tender. Stir in the cream and parsley.
Remove pot from heat. Use an immersion blender to process until you reach your desired consistency. You can also use a blender to purée the soup. Taste and season with more salt and pepper, as needed, and serve. Divide between bowls and garnish with a squeeze of lemon, olive oil and parsley.