Heat a medium saucepan over medium heat and add the olive oil. Once it shimmers, add the diced onion and cook for about 3-4 minutes until it becomes translucent and fragrant.
Add the minced garlic to the pan and cook for another 30 seconds until fragrant, being careful not to burn it.
Stir in the fresh peas and cook for 2-3 minutes, watching for their bright green color to intensify and smell sweet and fresh.
Pour in the vegetable broth, increase the heat to bring the mixture to a gentle boil, then reduce to low and simmer uncovered for 5 minutes until the peas are tender and brightly colored.
Remove the soup from heat and use an immersion blender to puree directly in the pot until smooth, or pulse in a regular blender in batches. The soup should be velvety and bright green.
Stir in the lemon juice and chopped mint leaves, then taste and season with salt and pepper as needed. The bright lemon and mint should lift the flavors.
Finish with a drizzle of good olive oil, then serve the soup warm, garnished with extra mint if desired.