Make the chive oil. Blanch the chives in boiling salted water for 30 seconds, then transfer immediately to an ice bath. Squeeze dry, then blend with the olive oil until vivid green. Strain through a fine-mesh sieve and set aside. This can be made a day ahead.
Soften the aromatics. In a medium pot over medium-low heat, melt the butter. Add the shallots and garlic with a pinch of salt and cook gently until soft and translucent, about 8 minutes. Don't let them color.
Simmer the peas. Add the stock and bring to a gentle simmer. Add the peas and mint and cook just until the peas are tender and bright green, about 3 to 4 minutes. Pull from the heat immediately to preserve that vivid spring color.
Blend until silky. Transfer the soup in batches to a high-powered blender and blend on high until completely smooth, about 2 minutes per batch. Pass through a fine-mesh sieve for an ultra-silky texture, if desired. Season with salt, white pepper, and a squeeze of lemon.
Chill or warm. Serve the soup warm straight away, or refrigerate and serve chilled — both are equally beautiful. If serving chilled, adjust seasoning again before plating as cold mutes salt and acid.
Plate and finish. Ladle into shallow bowls. Add a graceful swirl of crème fraîche, a drizzle of chive oil, a few drops of lemon juice, and a small handful of pea tendrils or microgreens. Serve immediately alongside a well-chilled glass of a Domaine Carneros wine.