Fill a large bowl with very cold water and add mussels and cornmeal. Leave uncovered and place in refrigerator for 1 hour. This allows the mussels to expel their sand and any grainy bits. Scrub mussels and rinse well. For optimal food safety, examine mussels and discard any that have a damaged shell or remain open and will not close by tapping lightly on the shell.
In a large skillet, melt butter and cook onion over medium-high heat until soft and translucent, about 10 minutes. Add garlic and cook until fragrant, about 2 to 3 minutes more. Add tomatoes, wine, salt, and pepper. Bring back to a boil over medium-high heat. Reduce heat to medium-low, cover and simmer for 30 minutes.
Uncover sauce and using a wooden spoon, break apart tomatoes into small pieces. Add mussels to simmering sauce. Cover and simmer until shells open and mussels are thoroughly cooked, about 5 to 7 minutes. Discard any mussels that do not open. Add heavy whipping cream and parsley, stirring until just combined.
Spoon mussels into 4-inch ramekins with plenty of sauce. Serve with crusty French baguette and garnish with parsley, if desired.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/mussels-white-wine-tomato-sauce/