Adjust an oven rack to the middle position and heat the oven to 400°F.

Trim the artichokes by cutting off the top inch of the crown and the stem. Use kitchen shears to snip off the thorny tips of the remaining leaves. Halve the artichokes lengthwise and scrape out the fuzzy choke with a spoon.

Arrange the artichokes cut-side down in a 13 by 9-inch baking dish. Place the lemon halves cut-side up next to them. Drizzle with oil and season with salt and pepper. Pour a small splash of water into the dish (about 1/4 cup) and cover tightly with aluminum foil.

Roast until the artichoke hearts are tender when pierced with a paring knife, about 45 to 50 minutes.

Remove the lemons from the dish and let them cool slightly. Squeeze the roasted lemons through a fine-mesh strainer into a bowl, pressing firmly on the solids to extract as much juice and pulp as possible.

Whisk the garlic, mustard, and salt into the lemon juice. Gradually drizzle in the olive oil while whisking constantly until the dressing is thick and emulsified. Stir in the parsley and season with pepper.

Serve the artichokes warm or at room temperature with the vinaigrette for dipping or drizzling.