Discard the stems of the artichokes, keeping on a length 5-6 cm. Peel the artichokes and cut them in half lengthways, sprinkle with the lemon juice , to avoid blackening, and boil them for half an hour or until softened.
For the dressing: Cut the lemon in slices 0.5 cm wide and put them in a screw-top jar. Add the extra virgin olive oil , the vinegar, the sugar, the thyme, salt and pepper. Shake well, until the dressing becomes homogenized. Let it stand for a while, at room temperature, to enrich the flavor. Boil the broad beans, until softened but not overcooked. Then put them in cold water, to preserve their bright color. You may peel the or leave the with their skin. Drain them. Put the garlic cloves in a small pan, sprinkle them with a little oil and bake them in a preheated moderate oven , 180°C, for 30-40 minutes.
Place the artichokes and the broad beans in a serving dish, cover with the dressing and decorate with the lemon slices. Add the capers and the bakes cloves of garlic and serve.