Melt butter in a medium saucepan over medium heat. Add leek, and cook until softened, about
4 minutes. Stir in potato and dry vermouth, and reduce slightly, about 2 minutes. Add chicken stock and water. Bring to a boil. Reduce heat, cover, and simmer until potatoes are tender, 7 to 8 minutes.
Bring to a boil. Add peas. Cover, and cook just until
peas are tender and bright green, about 2 minutes. Filling a blender halfway and covering with a kitchen
towel, puree soup in batches. Strain through a coarse sieve into a large bowl; discard solids. Stir in buttermilk, and season with salt and pepper. Chill soup for at least 3 hours or up to overnight.
Garnish each serving with pea tendrils if desired.
For another seasonal take, substitute 1 pound fresh asparagus, trimmed and cut into 1/2-inch pieces, for the peas.