In a large pot, heat the olive oil over medium heat.
Add the sliced leeks and sauté until they become soft and translucent, about 5-7 minutes.
Stir in the minced garlic and cook for an additional 1-2 minutes until fragrant.
Toss in the broccoli florets and diced potato, stirring to combine.
Add the vegetable or chicken broth to the pot, ensuring the vegetables are fully submerged.
Season with salt and pepper to taste.
Increase the heat to bring the mixture to a boil, then reduce to a simmer.
Allow the soup to simmer for 20-25 minutes, or until the broccoli and potato are tender.
Using an immersion blender or a regular blender, puree the soup until smooth. If using a regular blender, blend in batches and be cautious of the hot liquid.
If desired, stir in the heavy cream for a richer texture and flavor.
Taste the soup and adjust seasoning if necessary.
Ladle the soup into bowls and garnish with fresh parsley if desired.