2 bunches green garlic (about 1 pound)
4 tablespoons olive oil, divided
Kosher salt, freshly ground pepper
2 cups shelled fresh peas (from about 2 pounds pods) or frozen peas, thawed
1/3 cup heavy cream
Cut dark-green tops from green garlic and slice crosswise 1/2″ thick; slice bulbs and pale-green stalks crosswise 1/4″ thick.
Heat 2 tablespoons oil in a large saucepan over medium heat. Add bulbs and stalks, season with salt and pepper, and cook, stirring often, until beginning to soften, 8–10 minutes. Add tops and cook, stirring often, until soft, about 3 minutes.
Add 4 cups water to saucepan and bring to a boil. Add peas, reduce heat, and simmer gently until peas are bright green and tender, about 5 minutes.
Let cool slightly, then purée soup in a blender with remaining 2 tablespoons oil, adding water to thin if needed, until smooth. Strain soup through a fine-mesh sieve into a clean saucepan, pressing on solids; season with salt and pepper. Reheat briefly (to preserve color) before serving.
Add cream, salt and pepper to a whipped cream dispenser shake and serve soup with a swirl of whipped cream.