Step 1

Place potatoes in a medium saucepan. Add cold water to cover by 2". Add 1 Tbsp. salt. Bring to a boil; reduce heat to low and simmer until potatoes are tender, about 15 minutes. Drain; set aside.

Step 2

Meanwhile, heat oil in a large pot over medium heat. Add fennel, shallots, and garlic and cook, stirring often, until soft and fragrant, about 5 minutes. Remove pot from heat; add wine. Return pot to heat; increase heat to high, add littleneck clams, cover, and cook for 1 minute. Add mussels, cockles, razor clams (if using), and potatoes. Cover; cook until all shellfish have opened (discard any that do not open), 4–5 minutes longer.

Step 3

Using a slotted spoon, transfer shellfish and potatoes to a warm bowl and transfer any remaining vegetables from pot to a blender. Pour liquid from pot into blender, leaving any sediment behind. Add 1 cup parsley and butter to blender; purée on high until sauce is bright green and thickened, about 2 minutes. Season to taste with salt and pepper. Pour over shellfish; stir to coat. Garnish with whole parsley leaves.