Prep your aromatics. Cut the root end and dark green parts off your leek, then slice it in half lengthwise. Rinse between the layers to remove any sand or dirt (leeks are notoriously gritty). Chop the clean leek, onion, and garlic.
Start the base. Heat olive oil or butter in a medium pot over medium heat. Add the leek and onion with a pinch of salt and cook until soft but not browned, about 5-7 minutes. Add the garlic and cook for another 30 seconds until fragrant.
Add the stars of the show. Toss in the peas and give everything a good stir to coat with the oil. Pour in the vegetable broth and bring to a simmer. Cook just until the peas are tender, about 3-5 minutes if frozen, 5-8 minutes if fresh. Don't overcook or you'll lose that vibrant green color!
Work some blender magic. Remove the pot from heat and add the mint leaves and lemon juice. Using an immersion blender, purée the soup until smooth. Alternatively, carefully transfer to a regular blender in batches (be careful blending hot liquids—start slow and hold the lid with a kitchen towel).
Make it silky. If using cream, stir it in now. For an extra-smooth soup, strain through a fine-mesh sieve, pressing on the solids with a spoon (this step is optional but takes it to restaurant-quality).
Taste and adjust. Season with salt and pepper. If the soup is too thick, add a splash more broth. If it needs more brightness, add another squeeze of lemon.
Serve in style. Ladle into bowls and garnish with a dollop of crème fraîche or yogurt, a few reserved peas, fresh mint leaves, toasted nuts or seeds, and a drizzle of good olive oil.
Chill option. If serving cold, let the soup cool completely, then refrigerate for at least 2 hours or overnight. The flavor actually improves as it sits!