Spatchcock the chicken by cutting along both sides of the backbone with a sharp knife or pair of poultry shears. Place the chicken on a cutting board, breast-side up, and press down with your hands to flatten it. Pat the chicken dry with paper towel and transfer it to a sheet pan.
In a bowl, combine the olive oil, garlic, parsley, rosemary, thyme, lemon zest, lemon juice, smoked paprika, salt and pepper and stir to combine. Pour the marinade over the chicken and massage all over to evenly coat. Transfer the chicken to the refrigerator, uncovered, for 6 hours or overnight for best results.
Preheat the oven to 425F.
Add the squash to a sheet pan lined with parchment paper, drizzle with 2 tablespoons olive oil and season with ¼ teaspoon salt and ¼ teaspoon black pepper. Toss the squash to coat and arrange the wedges in a single layer with one of the cut sides down. Transfer the chicken and squash to the bottom rack of the oven and cook, undisturbed, until the chicken is golden and the thickest part of the breast registers around 160F and the squash is golden brown and fork-tender, around 45 minutes. Remove the squash from the oven, cover with foil to keep warm and set aside.
Switch the oven to broil, position the chicken on the top rack and cook until the skin is golden brown and crispy, 3 to 5 minutes. Remove the chicken from the oven and let it rest at least 5 minutes before carving.
To serve, arrange the Kale and California Grape Vinaigrette onto individual serving platters and top with two or three roasted squash wedges. Serve with the carved Lemon Herb Roast chicken and garnish with freshly-grated Parmigiano Reggiano.