Trim the root end and the dry dark green end from the green garlic, leaving just the white and light green parts. Peel away the toughest outer layer and slice the stem. If your green garlic has a fully-formed bulb, cut it away from the stem, then peel and dice the cloves like regular garlic.
In a medium saucepan, heat olive oil over medium heat. Add green garlic, chili flakes, and a pinch of salt, and sweat for 1-2 minutes, or until the garlic is soft and fragrant. Add peas, water, lemon juice, mint sprig, and salt to taste, and bring to a boil. Reduce the heat to low and simmer, uncovered, for about 10 minutes, or until the peas are soft but not mushy. Remove mint sprig and discard. Transfer the soup to a blender (or use an immersion blender) and puree until smooth.
The soup can be served warm or cold. Taste and adjust the seasoning before serving. The soup will keep in the fridge in an airtight container for up to 3 days.