In a medium pot over medium high heat melt butter. Add bacon and onions, celery and thyme sprigs. Season with salt, pepper and hot sauce and cook 5 minutes. Add flour and cook a minute more.
Add half-and-half and stock and bring to a bubble, then stir in potatoes and clams. Bring soup back to a boil, reduce heat and simmer 15 minutes, until potatoes are cooked and soup has thickened to coat the back of a spoon.
Heat toaster oven or broiler then toast split English muffins. While muffins toast, grind ham with paprika, hot sauce, mustard, and parsley in a food processor. Spread ham on toasted muffins. Top each muffin half with 2 slices Cheddar and melt cheese in toaster oven or under broiler.
Remove the thyme sprigs from the soup. The thyme leaves will have fallen off into the soup. Stir and adjust seasonings in your soup. Pour soup into mugs. Serve with deviled ham and cheese mug toppers.