Preheat your oven to 425°F (220°C). In a large bowl, toss the cut russet potatoes with 2 tablespoons of extra virgin olive oil, chopped garlic, salt, pepper, and sesame seeds. Spread evenly on one side of a large sheet pan. Roast for about 20 minutes, or until golden and crispy on the edges.
While the potatoes roast, combine basil pesto, finely chopped shallot, lemon zest, lemon juice, crushed red pepper flakes, and reserved sun-dried tomato oil in a large bowl. Add chicken pieces and toss to coat evenly. Marinate for at least 10 minutes.
Remove the sheet pan from the oven. Nestle marinated chicken pieces on the other half of the pan alongside the potatoes. Scatter chopped sun-dried tomatoes and fresh dill or thyme over the chicken and potatoes. Dot the butter over the potatoes. Return to the oven for 15-20 minutes, or until chicken is cooked through and potatoes are tender.
While chicken and potatoes finish cooking, combine feta cheese, plain Greek yogurt, and 2 tablespoons extra virgin olive oil in a food processor or blender. Blend until smooth and creamy. Adjust seasoning with salt or lemon juice if desired.
Remove the sheet pan from the oven. Serve pesto chicken and lemon butter potatoes warm with dollops of whipped feta and fresh pita or naan. Garnish with extra fresh herbs.