How to Make It
Preheat the oven to 425°. In a very large bowl, toss the chicken with the olive oil, garlic, lemon and thyme and season generously with salt and pepper. Arrange the chicken pieces skin side up on 2 large rimmed baking sheets and scatter the garlic and lemon around them.
Roast the chicken in the upper and lower thirds of the oven for about 45 minutes, rotating the pans halfway through, until an instant-read thermometer inserted into the thighs registers 165°. Transfer the chicken to a platter and let rest for 10 minutes.
Spread the walnuts on a baking sheet and bake for about 12 minutes, until golden and fragrant. Transfer to a food processor and let cool.
Add the basil and garlic to the food processor and pulse until finely chopped. Add the cheese and lemon juice and pulse until combined. With the machine on, add the olive oil until incorporated. Season the pesto with salt and pepper and transfer to a bowl. Serve the chicken with the walnut pesto.