For the cooking liquid, heat the olive oil in a large heavy-bottomed pan. Roughly chop the shallots and add them to the pan. Chop the garlic head in half across the cloves and add both halves to the pan, unpeeled, along with the thyme sprigs.
Roughly chop the plum tomatoes and add to the pan. Cook over a medium heat until the shallots are translucent but not browned.
Add the white wine and water and bring to a simmer. While the cooking liquid is simmering, prepare the artichokes.
Cut the artichoke in half, through the 'equator' with a serrated knife. Discard the tops of the artichokes. Remove and discard the stem and pull off the tough outer leaves at the base.
With a serrated knife, trim around the base of the artichoke to remove what remains of the tough outer leaves from the sides and base, removing all of the dark green to leave only the white part.
Carefully remove the hairy 'choke' in the middle of the artichoke with a spoon and discard. You'll be left with the artichoke heart or 'fond'. Scrape off any blackened, oxidised bits just before cooking.
Add the prepared artichoke fonds to the simmering cooking liquid, ensuring they're completely submerged (you may need to add more water). Simmer the artichokes for 6-8 minutes, until tender.
Meanwhile, prepare the mushrooms. Carefully clean the mushrooms and tear or slice them into pieces. Heat the olive oil in a pan over a medium heat, add the mushrooms and fry until browned.
Add the garlic and reduce the heat. Cook for a minute or two, until the garlic is lightly cooked. Transfer the mushrooms and garlic to a bowl and set aside.
When the artichoke fonds are tender, remove them from their cooking liquid and slice thickly. (You can keep the cooking liquid for 2-3 days in the fridge and use it another time.)
Fry the artichoke pieces in the same pan that the mushrooms were cooked in for a minute or two, until lightly browned.
For the dressing, zest the lemon and place the zest into a bowl. Juice the lemon and add the lemon juice to the bowl. Add the sherry vinegar.
Slowly add the olive oil and whisk constantly until thoroughly mixed. Add the grated parmesan and the salt and pepper and whisk to blend. Finely chop the garlic, add to the dressing and whisk to blend.
To assemble the salad, place the lettuce leaves in a bowl. Add the mushrooms, tomatoes, artichokes and enough lemon dressing to coat well. Mix thoroughly and serve.