To prevent the peas from losing their vibrant color once you've pureed them, the soup must be cooled very quickly.
In a large soup pot, heat the olive oil over low heat. Add the shallots and cook, covered, until they are soft and translucent. Add the stock and bring to a boil. Reduce the heat and simmer, uncovered, for 10 minutes.
Add the peas and simmer 10 minutes more for fresh peas and 4 minutes for frozen, or until the peas are just heated through and still vibrant.
Puree the mixture in a blender and pour through a wide-mesh strainer into a bowl set in a larger bowl filled with ice and cold water. Stir until cool to the touch.
Stir in the yogurt and season with salt and pepper. Divide among 4 chilled soup bowls and garnish with sprigs of tarragon.