Warm your large saucepan over medium heat and add a splash of olive oil, letting it shimmer as you prepare to sauté.
Add the finely chopped onion to the pan and sauté for about 5-7 minutes until it becomes translucent and fragrant, with a gentle sizzle and a soft, golden hue.
Stir in the fresh peas and cook for another 2 minutes just to warm them through, releasing their sweet aroma.
Pour in the vegetable broth, bringing the mixture to a gentle simmer. Let it cook for about 5 minutes until the peas are tender and vibrant green.
Roughly chop the fresh mint leaves and add most of them to the soup, reserving a few for garnish. Continue cooking for 1 minute to infuse the broth with herbal brightness.
Use your immersion blender directly in the pot to blend the soup until silky smooth, or carefully transfer in batches to a blender, blending until velvety and then returning to the pot.
Stir in the cream or coconut milk, then season with salt and pepper to taste. Warm the soup gently for 1-2 minutes until heated through, avoiding boiling.
Spoon the vibrant, velvety soup into bowls, garnishing with the remaining mint leaves and a drizzle of olive oil if desired. Serve hot and enjoy its fresh, comforting flavors.