Clean and Cook Mussels: Remove the byssus (green filament) from mussels and scrape impurities with a small knife. Place mussels in a pan, cover with lid, and cook for about 5 minutes, shaking occasionally until mussels open. Remove mussels to a bowl and strain the cooking liquid through a fine strainer, reserving the liquid.
Cook Clams: After purging clams in salted cold water for 1 hour, place clams in the same pan, cover, and cook for a couple of minutes, shaking occasionally until clams open. Remove clams to a bowl and strain the cooking liquid, reserving the liquid.
Prepare the Sauce Base: Clean the pan and heat a drizzle of olive oil. Add parsley stalks and garlic clove to create a fragrant soffritto. Add tomato passata and tomato paste, stirring and cooking gently for about 15 minutes.
Prepare Parsley Oil: Blend fresh parsley leaves with extra virgin olive oil until smooth to create a bright green, aromatic parsley oil. Set aside.
Cook Pasta and Combine: Cook linguine in boiling unsalted water until half done. Remove parsley stalks and garlic from sauce. Drain pasta and add it to the sauce pan. Add reserved mussel and clam cooking liquids to finish cooking the pasta in the sauce, stirring to create a creamy texture.
Finish and Serve: Turn off the heat and stir in the parsley oil. Add shelled mussels and clams, reserving some in shells for garnish. If sauce is too thick, add a little pasta water. Plate the pasta and decorate with mussels and clams in shells.