Heat oil in a medium saucepan over medium-high heat. Add onion and salt, and reduce heat to medium-low. Cook onion slowly, stirring often, until it is translucent and tender, about 15 minutes. Stir in diced pepper. Cook vegetables until the onion is pale golden and very soft, and the peppers are tender, about 15 more minutes.
While onions and peppers sweat, roughly chop tomatoes. Add tomatoes to cooked vegetables and increase heat to medium-high; bring to a boil. Lower heat and simmer sauce gently for 1 1/2 hours. Add reserved tomato juice as it reduces.
For the Paella Picada:
Mash the garlic in a mortar with a pestle until it is completely broken into a fine paste. Combine parsley and 2 tablespoons oil in a blender and process until finely chopped. Add just enough oil to create a thick paste, about 2 to 4 tablespoons more. Transfer herb paste to a medium bowl with garlic mixture. Stir pastes together. Season with salt to taste.
For the Aioli:
Mash the garlic and salt together in a mortar with a pestle until it is finely ground. Scrape garlic paste into a medium bowl with egg yolks and vinegar. Whisk together egg yolks and vinegar until combined. Stir in garlic paste. While whisking constantly, begin adding a few drops of blended oil.
As the base thickens, add oil a bit faster in a thin stream, continuing to whisk constantly. Season with more salt to taste, and thin with water if it is too thick.
For the Paella Salt:
Stir together all ingredients in a small bowl. Store, covered in an airtight container, at room temperature up to 3 days.
For the Fish and Squid Ink Stock:
In a large stockpot, combine all ingredients with 8 quarts water. Bring to a boil, skimming froth, then reduce heat and simmer, uncovered, 30 minutes to 1 hour. Pour stock through a fine-mesh sieve into a large bowl, discarding solids. Skim off any fat before using.