Begin to peel off leaves from around artichoke until you find thistle choke in the center.
Using a small knife, remove choke and throw it away.
Cut tough skin of stems and throw away.
Leave roughly 1 1/2 inches of stem on artichoke hearts.
Roughly chop hearts into small pieces, about 1/3 inch in thickness.
In a large pot over medium heat, melt butter and add artichoke hearts, leek, garlic and shallots.
Cook until tender but do not let them brown. About 1-2 minutes.
Add stock to pot and diced potatoes.
In cheesecloth, place bay leaf, thyme, mint and parsley, as well as the peppercorns, and add to pot.
Bring soup to a high simmer over medium-high heat, then lower back to medium heat.
Cook uncovered. About 1 1/4 hours.
Remove cheesecloth.
Using a handheld mixer, mix soup to desired texture.
Just before serving soup, heat to a simmer and stir in remaining butter and cream.
Season with salt and crushed black and red pepper to taste.
Serve with skewers of cooked shrimp.