Step 1Rinse chicken thighs and pat dry. (Do not remove any fat; it will add juiciness to the dish.)
Step 2In a large nonreactive bowl, combine the honey, vinegar, olive oil, oregano, 8 crushed garlic cloves, 1 teaspoon salt and one-fourth teaspoon white pepper, or to taste. Toss the chicken with the marinade. Marinate the chicken, covered and refrigerated, at least 2 hours, up to overnight, turning occasionally.
Step 3Heat the oven to 400 degrees. Transfer the chicken thighs to a large nonreactive baking dish. Place the chicken top-side down in the dish, then pour the marinade over. Roast the chicken until golden-brown at the edges and cooked through, 20 to 30 minutes. (The chicken will be firm to the touch, the juices will run clear, and a thermometer inserted will read 165 degrees.) Rotate the chicken halfway through roasting for even cooking.
Step 4While the chicken is roasting, prepare the pesto: In the bowl of a food processor, grind the pistachio nuts. Add the spinach and basil leaves, along with the 2 large cloves of garlic, and pulse to combine. With the processor running, gradually add the avocado (or olive) oil, and continue processing until the pesto is smooth. Remove the pesto to a bowl and stir in the grated lemon zest and lemon juice to taste, and season with one-half teaspoon salt and one-eighth teaspoon white pepper, or as desired. (The pesto can be made up to 1 day ahead and stored, refrigerated, in an airtight jar or container.)
Step 5To serve, place 1 to 2 chicken thighs on each plate and top each with a round dollop of pesto. Garnish with coarsely ground black pepper and a sprig of oregano, if desired.