Adjust an oven rack to the middle position and heat the oven to 450°F. Toss the prepared artichokes with oil and salt in a 9 by 13-inch baking dish, then arrange them cut-side down.

Trim the ends off the lemons so they can stand upright. Halve them crosswise and arrange them cut-side up in the baking dish next to the artichokes.

Cover the dish tightly with foil and roast for 15 minutes. Remove the foil and continue to roast until the artichoke hearts are tender when pierced with a knife and the cut sides are deeply browned, about 15 to 20 minutes longer.

Transfer the artichokes to a serving platter. Let the roasted lemons cool slightly until they can be handled, then squeeze them through a fine-mesh strainer set over a small bowl. Press firmly on the solids to extract as much juice and pulp as possible.

Whisk the garlic, mustard, salt, and pepper into the lemon juice. Whisking constantly, gradually drizzle in the olive oil until the dressing is thickened and emulsified.

Stir in the parsley. Spoon the vinaigrette over the warm artichokes and serve immediately.