Preheat the oven to 425°F.
Place the potatoes in a microwave-safe bowl with 1/2 cup water, cover loosely, and microwave for 4–5 minutes until just barely fork-tender, but not fully cooked through. Drain well and pat dry.
Toss the par-cooked potatoes with 1 Tablespoon of olive oil and 1/2 teaspoon of salt. Spread the potatoes in a single layer on a large lined sheet pan and roast for 10 minutes.
Meanwhile in a large bowl, whisk together 3 Tablespoons of olive oil, minced garlic, the remaining 1 teaspoon salt, black pepper, Italian seasoning, red pepper flakes, lemon zest, lemon juice, and 3 Tablespoons pesto.
Add the chicken thighs to the marinade. Massage the marinade into the chicken to evenly coat, then set aside while the potatoes cook (or marinate up to overnight in the fridge).
On a separate sheet pan, add the halved fresh peaches cut-side up and spray with a bit of oil. You may want to line the sheet pan with a little foil to prevent caramelization right on the pan!
When the timer for the potatoes goes off, nestle the chicken among them on the same pan. Add both pans to the oven and roast for 12-15 minutes. The potatoes should be starting to turn golden on the cut sides, the peaches softening and caramelizing at the edges, and the chicken just turning golden on top.
Pull the pans out (set the peaches aside) and divide 1/2 cup of the pesto evenly over each of the chicken thighs. Add in the cherry tomatoes.
Return the chicken pan to the oven for another 12-15 minutes, until the chicken reaches an internal temperature of 165°F, the tomatoes are soft, and the potato edges are crispy and golden.
Remove the pan from the oven, add the peaches back in, and scatter the fresh mozzarella (torn into chunks) across the pan, tucking pieces near the chicken and potatoes.
Tear the fresh basil leaves generously over the top and serve straight from the pan along with the remaining leftover peaches.
Serve with crusty bread to soak up the pan juices - so good!