Trim and discard tough woody ends from asparagus. Cut stalks into 1-inch pieces and set aside.
Meanwhile, pour olive oil in a blender and add chopped chives. Blend until well combined. Pour oil through a cheesecloth lined strainer into a bowl, discarding any solid chives. The oil will keep, refrigerated, for a few weeks.
Heat the 2 tablespoons olive oil in a large saucepan over medium heat. Add leek and cook until soft and translucent, stirring occasionally, about 10 minutes. Add stock and thyme and bring to a gentle simmer. Add asparagus and peas and cook until tender but still bright green, about 5 minutes.
Remove from heat, discard thyme sprigs, season well with salt and pepper and purée in batches until smooth. Transfer soup to a clean pot, stir in cream and heat until warmed through. Serve immediately (or chill until ready to serve), topped with whipped or sour cream, pea shoots and chive oil.