Trim the artichokes of their tough outer leaves, cut in half, and remove the fuzzy choke from the center.
Rub the cut surfaces with lemon so they don't brown.
Blanch in boiling salted water for 2 minutes, drain, then cool in cold water.
In a saucepan, fry the sliced carrot, parsley root and onion in the butter, add the white peppercorns, add the broth, and season with salt.
Add the artichokes, cover, and braise over low heat until completely tender, about 15-20 minutes.
Meanwhile, for the sauce, lightly fry the flour in the butter, add the broth, and cook until thick.
In a separate pan, fry the finely chopped mushrooms in butter until they release their liquid; once it has cooked off, add the cognac, and cook a little longer until the alcohol evaporates.
Add the mushrooms to the sauce, remove from the heat, and stir in the butter, the whipped cream and the lemon juice.
Season with white pepper and salt, carefully, so the sauce doesn't split.
Place the braised artichokes on a platter, and pour or serve the mushroom-butter sauce around or alongside them.
Based on: Malatinszky Fanny szakácskönyve (a classic Hungarian cookbook), modernised. Calories and protein are estimated.