Special equipment: Cheesecloth Kitchen twine
For the stock: In a piece of cheesecloth, place the garlic, bay leaves and thyme in the middle, and fold to make a sachet (also called a bouquet garni). Secure the bouquet with twine.
In a large stock pot, add the oil. Over medium-high heat, saute the carrots, onions, fennel and celery until slightly caramelized and tender, about 10 minutes. Deglaze with the clam juice. Then add in the shrimp shells, stirring constantly. Cook until the shells change color, about 3 minutes. Add in the tomato paste and cook until the paste changes from bright red to more of a rust color, another 5 minutes. Add in the sachet, tomatoes and saffron, stirring to combine. Reduce the heat to low and cook, stirring occasionally, 6 hours.
Remove and discard the sachet. In batches, puree the stock in a blender and strain through a fine mesh strainer. Gently push with a spoon or small ladle to extract as much liquid as possible, discarding any solids.
For the potatoes: Preheat the oven to 350 degrees F. Fill a baking tray with a 1/2-inch even layer of salt. In a large bowl, toss the potatoes with the oil and a few turns of cracked black pepper. Place the potatoes on the salt bed in an even layer. Roast until fork tender, about 1 hour.
Cool the potatoes slightly and brush off any remaining salt.
For the stew: In a large pot with a lid, heat the oil and add the clams, cook for about 1 minute with the lid on. Add in the mussels and wine, cooking with lid on until they both open, 2 to 5 minutes depending on your range. Once opened, remove the lid, add the fish and cook for about 3 minutes, stirring constantly. Add in 8 cups of the stock and the potatoes, and cook until hot through. Season with salt and pepper. Reserve any remaining stock for another use.
Evenly divide among 4 bowls and serve with a slice of toasted sourdough. Serve immediately.
Cool the stock completely before storing. Store any leftover stock in an airtight container for up to 5 days in the refrigerator or a month in the freezer.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.