Use a mixer, fitted with the whisk attachment, and combine egg yolks, garlic, saffron, and a pinch of salt; whisk at high speed, while adding oil, drop by drop (this is important because otherwise mixture will not thicken properly).
As the aioli begins to thicken you can increase the oil to a thin stream; adjust seasonings with a squeeze of lemon juice and/or more salt, if needed.
In a paella pan with lid or large deep-sided skillet, heat olive oil over medium heat; add onion and saute until softened and golden, about 15 minutes.
Meanwhile, coarsely grate the tomatoes, cut side, until only the skins remain and discard skins; you should have about 2 cups of tomatoes.
Stir the tomatoes, peppers, and bay leaves into the onions; season with paprika.
Simmer, stirring occasionally, until most of the liquid evaporates, about 15 minutes.
Add the stock, bring to a boil, then stir in the rice; reduce heat to medium and simmer 10 minutes, stirring to prevent the rice from sticking.
Stir in the peas, squid, mussels or clams, and shrimp; turn heat to low and simmer until nearly all the liquid has evaporated, about 10 minutes.
Cover with lid, remove from heat, and let rest 5 to 10 minutes; sprinkle with parsley and let cool.