Preheat a 2- or 3-qt. sauté pan over medium-high heat until rim of pan is hot to the touch. Add 2 Tbsp. oil and heat for about 1 minute.
Add onion and cook, stirring occasionally, until soft and beginning to brown, about 3 - 5 minutes. Add tomatoes and tomato paste; continue to cook, stirring often, for 5 minutes. Pour in wine and cook, stirring occasionally, until mixture is reduced by half, about 5 minutes. Pour in fish stock; again cook until reduced by half, about 5 minutes.
Pour tomato mixture into a food processor or blender; process until smoothly puréed. Transfer sauce to a bowl, season to taste with salt and pepper and set aside. (At this point, you may cover and refrigerate for up to 24 hours.)
Pull beard from each mussel with a swift tug.
Preheat a 13-in. paella pan or 5-qt. sauté pan over medium-high heat until rim of the pan is hot to the touch. Add remaining 2 Tbsp. oil and heat for about 1 minute. Add garlic, 2 Tbsp. parsley and mussels. Increase heat to high, cover pan, and cook until mussels pop open, about 5 - 8 minutes.
With a slotted spoon, transfer mussels to a bowl; keep warm. Discard any unopened mussels.
Add tomato sauce to liquid in pan and cook, stirring often, until reduced by about a fourth, 3 - 5 minutes.
Return mussels (and any liquid that has accumulated in bowl) to pan. Mix quickly to reheat mussels and coat them with sauce.
Ladle mussels into warm shallow individual bowls. Sprinkle with remaining parsley.