Add the garlic, turnip greens, basil leaves, parsley and lemon zest to the bowl of a food processor. Pulse until the leaves are broken up into very small pieces.
Add the walnuts and pulse 5-6 more times until they have broken up.
Add the nutritional yeast and olive oil. Blend until a smooth paste forms. Season with salt to taste.
Can be made up to 3 days ahead.
FOR THE CHICKEN:
Preheat oven to 400° F.
Pat the chicken as dry as possible. Take 3⁄4 cup of the pesto and rub all over the chicken as well as under the skin. Season liberally with kosher salt. Allow to rest at room temperature for 30 minutes.
Evenly butter all four slices of bread and place the cut side down into a cast iron skillet. Place the chicken on top of the bread, breast facing up. Place in the oven and cook for 25 minutes. Remove from the oven and place the chicken onto a cutting board. Turn each slice of bread over to the other cut side. Return chicken to the pan. Place back in the oven and cook for another 20 minutes or until an instant read thermometer reads 155° F when inserted into the thickest part of the breast.
Remove the chicken and bread from the skillet and set back onto the cutting board, cover loosely with aluminum for and let rest for 20 minutes.
Meanwhile, add the turnips to the same pan the chicken was cooked in. If the pan is a little dry add a drizzle of olive oil. Season the turnips with sea salt and cook in the oven for 15 minutes.
FOR ASSEMBLY:
I love the dramatic presentation of serving this dish in the cast iron skillet it was cooked in. Cut each slice of bread in half and arrange in the skillet. Arrange the turnips next to the bread. You can then either serve the chicken whole and carve it at the table or break it down into 8 pieces; thighs, legs and each breast cut in half. Serve with remaining pesto and garnish with pea shoots.