Slice the andouille into quarters from end to end, then slice about as thick as two stacked nickels. Put them into a large saucepan over medium-low heat, and cook--stirring only once or twice--until the excess fat is rendered out.
Remove the andouille with a slotted spoon and drain on paper towels. Pour off the excess fat from the pan but don't wipe the pan.
Add the onion to the saucepan and cook until translucent.
Add the stock (or water), the red potatoes and the sweet potatoes. Add the stock and enough water to cover everything. Bring it to a boil and cook about fifteen minutes.
Strain the saucepan contents. Return the liquid to the pan. Process the solids in a food processor to a rough puree. (Or, better, run it though a food mill.) Add it back to the saucepan and return to a simmer.
Over a plate to catch all the milk, cut the corn krenels off the cobs. Scrape the cobs to get all the milk. Add all the kernels and milk into the saucepan.
Stir in the cayenne, Worcestershire, salt, brown sugar, and whipping cream. Add the andouille. Taste the soup and adjust with salt and Tabasco to taste. If the soup is too thick, add water.