In a large pot, heat the olive oil and add the chopped shallots and leeks.
Sauté over medium heat until translucent, but not yet browned (7-10 minutes).
Add the garlic and sauté for about another minute, until fragrant.
Add the vegetable broth and diced potatoes and cook, covered, for about 10 minutes or until the potatoes are just tender.
While the potatoes are cooking, make the crispy ham strips (see below).
Add the peas and cook for about five to ten minutes more (fresh peas will need at least the full five minutes, while frozen peas only need a couple of minutes to warm up).
Take the soup off of the heat and add the fresh mint leaves. Puree the soup in batches in a traditional blender, or use an immersion blender directly in the pot. Make sure the soup is completely smooth.
Add a tablespoon of cream if you wish, for an even more indulgent soup.
Season with sea salt and freshly cracked black pepper.
Top your pea and mint soup with crispy ham and enjoy!