Sieve this soup because it becomes clear and light. Sieving is not absolutely necessary, but I like it a lot better this way.
If you make your own chicken stock, make sure to flavor it with salt and pepper. When you use store-bought stock, most of the time, that isn't really necessary.
Pour the cream into the bowls and not into the pan. It can curdle when you do the latter. Besides that, you can store this soup only without the addition of cream. That way this soup keeps well in the refrigerator for 2 days and 3 weeks in the freezer.
Chop the shallot finely.
Melt the butter over low heat in a saucepan and add the shallot.
Fruit the onion until it's glazy (about 3 minutes).
Pour in the broth and bring to a boil.
Reduce heat to low and add the peas to the soup.
Allow simmering for 25 minutes until the peas are tender.
Meanwhile, slice the chives fine.
Cut the ham into thin strips.
Puree the soup with a blender and sieve.
Heat the soup until it's hot.
Pour into a bowl, drizzle half a spoonful of heavy cream in the middle of the soup.