Set aside 1/2 can of peas from 2 cans (11 oz) tiny peas.
Heat 2 tbsp unsalted butter and sauté 1 medium onion finely chopped, and 1 small carrot chopped and cook vegetables until onion is translucent. Add 1/2 tsp tarragon leaves 1/2 tsp thyme and season with kosher salt and black pepper.
Add 1/4 lb cooked ham, 3-4 iceberg lettuce leaves, peas along with liquid from can, plus 2 cups water or enough water to cover by 2".
Bring to a boil then reduce heat and simmer for 30 minutes.
Cool, remove ham and puree soup in blender.
Return to pot and add remaining peas, reserve until ready to serve.