Step 1Baby artichokes don't need trimming. With the other artichokes, cut off the top quarter, about 1 inch of large or 1/2 inch of small ones, using a sharp, heavy knife or a serrated knife. Trim the spikes from the tips of the leaves with scissors. With baby artichokes, leave the stems attached. With others, cut off the stems and peel off their fibrous outer layer with a paring knife. Wash your hands and the board after handling raw artichokes, or the next foods you handle or cut will have a funny taste.
Step 2Place the artichokes and stems in a large saucepan of boiling salted water and cover with a lid of slightly smaller diameter to keep them submerged. Cook over medium heat until a leaf near the bottom can be easily pulled out, but don't cook them until mushy. Small ones need about 15 to 20 minutes, medium ones about 25 to 35 and large artichokes about 45 minutes.
Step 3Using tongs, remove the artichokes and set them upside down in a colander to drain. (Don't save the cooking liquid; it doesn't taste good.)
Step 4Either cover them to keep them warm, or let them cool and serve them at room temperature or chilled. Accompany them with bowls of dipping sauce.
Step 1Whisk the mustard in a bowl with the vinegar, and salt and pepper to taste. Gradually whisk in 1/2 cup of oil. Taste, and add more oil if the dressing is too sharp. Stir in the shallot and parsley. Taste and adjust the seasoning. Whisk again before serving.
Step 1Blend the garlic (but not the garlic chives) and the lime juice in a food processor. Remove 1 chile from its adobo sauce, add the chile to the processor and blend it to a puree. Add the mayonnaise and process until blended. Taste; if you want more heat, add 1 teaspoon of the adobo sauce or dice another chile, add it to the sauce and process until well blended. Transfer the dip to a bowl. Add salt and more lime juice if needed. Add the cilantro and the garlic chives, if using.