Place an oven rack in the lower-middle position and heat the oven to 450°F. Bring 4 quarts of water and the salt to a boil in a large pot. On a rimmed sheet pan, use your hands to gently toss the artichokes with 3 tablespoons of the oil until evenly coated, then spread into a single layer, cut side down. Transfer to the oven and roast until deeply browned on the bottom, 18 to 22 minutes, rotating the pan halfway through.

Add the pasta to the boiling water and cook for 2 minutes less than the low end of the package instructions.

Meanwhile, heat the remaining 4 tablespoons (¼ cup) of oil in a large, high-sided skillet over medium heat. Add the garlic and cook, stirring constantly, until fragrant and just starting to brown, about 1 minute; remove the pan from the heat.

Use a mesh spider to transfer the pasta directly to the skillet and return to medium heat. Add 1½ cups of the pasta cooking water, the preserved lemon, capers, pepper, and three-quarters of the roasted artichokes (choose the lighter- colored artichokes to stir in, reserving the more browned ones for topping). Cook, tossing and stirring to combine, until the sauce thickens and clings to the pasta but still pools slightly in the pan, 3 to 5 minutes.

Remove the pan from the heat and stir in the parsley and Pecorino. Transfer the pasta to a serving dish or individual bowls, top with the remaining artichokes, and serve.