Heat a large pot over medium heat and add a tablespoon of olive oil. Once shimmering, smell the fragrant aroma and see the oil glisten.
Add the fresh or frozen peas to the pot. Stir gently, watching them turn bright green and release a sweet aroma, about 2-3 minutes.
Pour in the vegetable stock, ensuring the peas are covered generously. Bring to a gentle simmer, then reduce heat to low, cover, and cook for about 8-10 minutes until peas are tender and luminous.
While the peas cook, tear the fresh mint leaves and set aside. Once the peas are tender, add the mint to the pot. Stir and let steep for 2 minutes until the aroma of mint fills the air.
Remove the pot from heat. Use an immersion blender or carefully transfer the mixture in batches to a blender. Blend until the soup is silky smooth, about 30 seconds per batch, and be cautious with hot liquids.
Return the blended soup to the pot if needed. Stir in the heavy cream or coconut milk, warming gently over low heat for 2 minutes without boiling, to meld flavors and add richness.
Taste the soup and season with flaky sea salt and freshly cracked black pepper. Squeeze in the lemon juice and stir well to brighten the flavors.
Let the soup rest off heat for 2 minutes, then ladle into bowls. Garnish with reserved mint leaves or a drizzle of olive oil for extra aroma, and serve warm.
