For the garlic-herb dressing:
1) Preheat the oven to 200C/Gas 6. Cut a piece of aluminium foil about 30cm long.
2) Put the garlic on 1/2 of the foil, sprinkle with salt and pepper, drizzle in some olive oil, and add 2 sprigs of thyme. Fold the foil enclosing the garlic, making a pouch, and add a couple teaspoons of water. Fold the foil back over the garlic to enclose and fold in the edges 2 or 3 times to seal. Put the package in the oven and roast for 30 minutes, or longer, until the garlic is soft.
3) Open the package and let the garlic cool a bit, then squeeze out the cloves into a food processor or blender. Add 125ml olive oil, the lemon juice, parsley, and thyme leaves and puree to make a thick vinaigrette dressing.
For the grilled chicken and radicchio:
1) Preheat a barbecue or griddle to a medium heat.
2) Rinse the chicken and pat dry with paper towels. Put the pieces in a bowl, sprinkle with salt and pepper, and drizzle with olive oil; toss to coat with the seasoning and then refrigerate while you get everything else together.
3) Put the radicchio in another bowl, drizzle with olive oil, balsamic vinegar. Sprinkle with salt and pepper and toss; set aside.
4) When you're ready to cook, take a few paper towels and fold them several times to make a thick square. Blot a small amount of oil on the paper towel and carefully and quickly wipe the hot grates of the griddle to make a nonstick surface.
5) Season with salt and pepper and place the radicchio quarters on the preheated griddle. Cook the radicchio for about 2 minutes per side until it has a nice char; pull it off the griddle, place into a bowl, cover with cling film, and set aside to steam and finish cooking.
6) Then put the chicken on the griddle, skin side down, and griddle. Griddle the chicken for about 20 minutes, turning once, then baste with about half of the vinaigrette and keep cooking until an instant-read thermometer stuck into the thickest part of the thigh reads 72 degrees C and the chicken is nice and caramelised all over, 15 to 20 more minutes. During the last few minutes, throw the lemon halves on the griddle, cut sides down, and cook until just marked and smoky.
7) To serve, separate the radicchio into individual leaves in a big bowl. Add the chicken and the rest of the dressing and toss well. Serve with grilled lemon halves, squeeze the lemon over the chicken, and top with reserved dressing.