Step 1In a bowl or measuring cup, combine the dried mushrooms with the boiling water. Set aside until the mushrooms are reconstituted and softened, about 20 minutes. Line a strainer with cheesecloth and place over a bowl. Drain the porcinis through the strainer and squeeze them to extract the flavorful liquid, saving the liquid. Rinse thoroughly if the porcinis are sandy and squeeze again. Coarsely chop and set aside.
Step 2Add enough broth to mushroom broth to measure 5 cups.
Step 3Massage the saffron with your thumb and fingers and place in a ramekin or small bowl. Cover with 2 tablespoons hot water.
Step 4Prepare the artichokes: Break away all tough outer leaves from artichokes, then trim to expose tender bottoms. Cut into quarters, removing the chokes if they have developed, and cut in wedges no thicker than 1/2 inch at the thickest point. Place in a bowl of water acidulated with lemon juice. When ready to use, drain and dry on paper towels.
Step 5Heat 2 tablespoons of the oil in a 12-inch skillet or 12- to 13-inch paella pan over medium heat. Add the onion and cook, stirring often, until tender, about 5 minutes. Add the artichokes and cook, stirring, until beginning to color, about 3 minutes. Season with 1/4 teaspoon salt, or to taste.
Step 6Add the fresh mushrooms. Cook, stirring often, until the mushrooms begin to sweat. Scrape the bottom of the pan as mushrooms release their liquid to deglaze. Add the garlic and chopped reconstituted porcinis and continue to cook, stirring often, until the garlic is fragrant and the mushrooms and artichokes are tender. Season with 1/4 teaspoon salt and several grinds of pepper, or to taste. Remove to a bowl.
Step 7Add the remaining oil to the pan, and when hot, add the rice. Stir over medium heat until the rice begins to crackle and is thoroughly coated with oil. Continue to cook until the rice feels heavy and begins to stick to the pan, 3 to 4 minutes. Stir the artichoke-mushroom mix back into the rice, add the saffron, the broth (rinse out the ramekin with a little broth), and salt to taste (this will depend on the saltiness of your broth; the rice should be well seasoned). Add the white beans, bring to a boil and stir once. Reduce the heat to low and simmer until the broth has been absorbed, 20 to 25 minutes.
Step 8Leave the paella over the heat until the rice begins to stick to the bottom, about 5 minutes. Remove from heat and cover tightly. Set the paella aside to rest for 10 minutes. Check the rice at the edges of the pan and, if not quite chewy enough, stir toward the middle, cover again and set aside for another 10 minutes.
Step 9Drizzle a little olive oil over the top and sprinkle with parsley if desired. Serve, passing aioli at the table for guests to spoon on.