How to Make It
Squeeze the lemon halves into a large bowl of water. Working with 1 artichoke at a time, snap off all of the outer leaves and trim the stem so the artichoke will stand upright. With a small, sharp knife, cut 1/2 inch off the top and peel the base. With a melon baller, scoop out some of the choke to form a cup with a 1/4-inch rim. Drop the artichoke into the lemon water.
Drain the artichokes and pat dry. Heat the oil in a large, deep skillet. Add the artichokes and cook over moderately high heat, turning occasionally, until lightly browned, about 4 minutes. Add the carrot, celery and onion, season with salt and pepper and cook for 1 minute longer. Add the wine, vinegar, peppercorns, coriander seeds, bay leaves and thyme. Cover with parchment paper and a tight-fitting lid and simmer over moderately low heat, turning once or twice, until the artichokes are tender and the liquid has reduced slightly, about 30 minutes. Transfer the braised artichokes to a large platter to cool. Remove the bay leaves and thyme sprigs then season the cooking liquid with salt and pepper and reserve.
In a small bowl, mix the crème fraîche with the lemon juice and chives. Fold in the crabmeat and season lightly with salt and pepper. Using a small spoon, fill the cooled artichokes with the crab salad; arrange on a platter. Drizzle with the reserved cooking liquid and serve.