In a medium saucepan, bring the stock to a gentle simmer over medium heat.
Make a picada by mashing the garlic, saffron, and 1/8 teaspoon of the salt to a fine paste in a mortar with a pestle. Gradually add the parsley leaves, mashing each addition completely before adding more, until you have a green paste. Stir in 1/2 tablespoon of the olive oil and a few spoonfuls of warm stock to loosen the mixture so it is just runny enough to slowly drip from the spoon.
In a 12-inch paella pan, heat the remaining 2 tablespoons oil over medium-high heat. When the oil is shimmering, add the chicken, squid, and chorizo. Cook, tossing, until the chicken and squid begin to shrink and turn opaque, 1 to 2 minutes. Stir in the rice until it is shiny with oil, then add the picada, sofregit, pimentón, black pepper, and remaining 1/2 teaspoon salt. Add about 3 cups of hot stock to the pan, shaking it to settle and loosen any rice clusters as the stock begins to boil. Only shake the rice at this point; if stirred, it will become sticky.
Reduce the heat to medium-low and simmer the paella until about 80 percent of the liquid is absorbed, about 10 minutes. When most of the liquid is absorbed, the rice will start to sizzle a bit, almost as if it is asking you for another drink. At that point, add about 1 cup more stock by drizzling it around the edge of the pan so the stock seeps from the pan edge to the center.
Arrange the clams and mussels around the outer edge of the pan, and bury the shrimp throughout the rice. Simmer until about 80 percent of the liquid is absorbed and the rice starts to sizzle again, 5 to 6 minutes more. Drizzle about 1 cup more stock around the pan edge, and scatter the peas and green beans over the rice. Continue to simmer the rice until it is just beginning to become tender, 5 to 6 minutes more. At this point, the shrimp should be pink, the vegetables cooked through, and the clams and mussels should be open. Test the rice by taking a bite. The paella is done when the rice is plump, glossy, and tender on the surface with a firm white center when bitten into.
The edge of the paella pan should also have a dark rim of oily starch, which is a good sign of the crispy socarrat below. To test the socarrat, use a spoon to scrape the bottom of the paella pan. If the spoon doesn’t move through the rice but instead the rice is firm and the pan moves, then the socar rat has begun to form. When the socarrat has begun, rotate the pan for even browning. The rice will talk to you as it cooks; the crackle will get faster as the rice dries out, then it will go silent when the socar rat is finished forming. Your nose will tell you if it’s beginning to burn; just add a spoonful of stock to the scorching spot if so.
Serve the paella at the center of the table with spoons for guests to serve themselves and lemon wedges for squeezing.