Chicken al Mattone with Thyme Pesto

Name: Chicken al Mattone with Thyme Pesto
Ingredients: 1 whole chicken (3 to 4 pounds), rinsed and patted dry, and backbone removed; 4 tablespoons fresh lemon juice; 3 tablespoons olive oil; 2 tablespoons fresh thyme or lemon thyme leaves; 2 cloves garlic, chopped; 1 pinch salt and freshly ground black pepper; 1 1-foot-square paving stone wrapped in aluminum foil (use a cast iron skillet if you can't find one); 1 lemon, cut into wedges; 1 1/2 cups Italian flat-leaf parsley; 1/2 cup thyme leaves; 1/2 cup Parmesan cheese, grated; 1 lemon, zested; 1/2 cup toasted walnuts; 2 garlic cloves; 1/2 cup extra-virgin olive oil