Heat a medium saucepan over medium heat and add a tablespoon of olive oil until shimmering, then add the finely chopped onion. Sauté for about 5 minutes until translucent and fragrant, with a gentle sizzle and a slight golden hue.
Add the minced garlic to the onion and cook for 30 seconds until fragrant, with a sharp, aromatic aroma filling the air. Be careful not to let it brown too much, as it can turn bitter.
Pour in the vegetable broth and bring it to a gentle simmer. Let it cook for 10 minutes, allowing the flavors to meld and the onion to soften further.
Add the fresh peas to the simmering broth. Cook for 2-3 minutes until they turn bright green and tender but still vibrant, releasing their grassy aroma.
Using a slotted spoon, transfer the cooked peas and some broth into a blender. Puree until smooth and velvety, about 30 seconds, then repeat with remaining peas if necessary.
Return the blended soup to the saucepan and warm over low heat. If it feels too thick, stir in a splash of hot water or broth until it reaches your desired consistency.
Stir in the cream or coconut milk if using, and add a teaspoon of lemon juice to brighten the flavor. Taste and season with salt and pepper as needed.
Ladle the hot, velvety soup into bowls. Finish with a drizzle of olive oil or a sprig of fresh herbs if desired, and serve immediately while warm.
