For the sauce, thinly slice 6 of the shallots. Heat the oil in a heavy-bottomed pan. Sweat the shallots and half the thyme with a pinch of salt and butter until translucent.
Add the wine and reduce until a syrup consistency then add in the veal stock and season. Pass through a fine sieve and reduce to a sauce consistency.
Meanwhile, peel off the dry outer leaves of the artichokes and discard. Cut off the top and peel into the heart with a small paring knife. Mix the lemon juice with cold water and keep the peeled artichokes in the water to keep their colour.
Dice the ham and remaining shallots. Drain the artichokes. Use a mandolin to thinly slice the artichokes lengthways. Sweat the ham and shallots in the remaining butter and add the sliced artichokes (keep a few slices for garnish).
Slice the burrata in half and season with olive oil, salt and a twist of black pepper.
Spoon the cooked artichoke over the burrata and finish with the sauce. Dress a few slices of raw artichokes with olive oil and garnish on top.