Put whelks or periwinkles into a deep medium-size pot, and cover with 1-2'' of cold water. Cover pot, and bring to a boil over high heat. Reduce heat to medium, and cook about 15 minutes.
Transfer whelks or periwinkles to a bowl with a slotted spoon, reserving broth, and let them cool until cool enough to handle. If using whelks, pry out of shells with an ice pick or a fork. Cut off dark, bony disk that covers the opening into the shell, scrape off and discard skin and black intestines, then rinse. If using periwinkles, use a straight pin or the tip of a paring knife to remove meat from shell, then pull off and discard intestine and small membrane. Discard shells, and set meat aside.
Melt shortening in a medium heavy-bottomed pot over medium heat, add onions and garlic, and cook until onions are soft, about 10 minutes. Add flour, and cook, stirring constantly with a wooden spoon, until lightly browned, about 4 minutes. Add tomato paste, and fry for 2 minutes, then gradually add reserved broth, whisking constantly to prevent lumps. Reduce heat to medium-low, then add parsley, thyme, and potatoes. Add whelks or periwinkles, then season to taste with salt and pepper. Cook stew, stirring occasionally, until potatoes are soft, whelks or periwinkles are tender, and sauce has thickened, about 50 minutes. Serve with a crusty baguette, if you like.