In a large pan, melt the butter or heat the olive oil over medium heat. Add the chopped onion and minced garlic. Sauté until the onion becomes translucent and the garlic is fragrant.
Add white wine to the pan. Allow the wine to simmer for a minute or two, which helps cook off the alcohol and allows the flavors to blend with the other ingredients.
Stir in the tomato paste and cook for a minute or two, allowing the flavors to meld together.
Add the mussel meat to the pan and toss to coat it with the onion and tomato mixture. Cook for a couple of minutes to heat the mussel meat through.
Reduce the heat to low and pour in the heavy cream. Stir well to combine all the ingredients. Allow the mixture to simmer gently for a few minutes, stirring occasionally.
Season the creamy mussel meat with salt, pepper, and dried oregano (or other herbs of your choice). Adjust the seasoning to your taste preferences.
Once the sauce has thickened to your desired consistency and the mussel meat is heated through, remove the pan from the heat.
Serve the creamy mussel meat in bowls. Garnish with freshly chopped parsley and enjoy with toasted ciabatta.