Heat the oven to 400°F. Toss the potato pieces with 2 tablespoons olive oil, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Spread them in a single layer on a rimmed baking sheet and roast until fork-tender and golden at the edges, about 22–25 minutes, turning once halfway through.
While the potatoes start roasting, pat the chicken dry and season both sides with 1/4 teaspoon salt and 1/8 teaspoon black pepper. Warm 1 tablespoon olive oil in a large skillet over medium-high heat and sear the chicken 2–3 minutes per side, just until nicely browned (it will finish cooking in the oven). Transfer the seared pieces to a plate.
In a bowl, combine the halved cherry tomatoes with 2 cloves minced garlic, the lemon zest, lemon juice, pesto, and the red pepper flakes if using. Season with a pinch of salt and toss gently—this will be the fresh, saucy element for the pan.
When potatoes are just about done, reduce oven temperature to 375°F. Push the roasted potatoes toward the edges of the sheet pan to make room in the center. Scatter the tomato mixture into the middle of the pan and nestle the seared chicken on top of the tomatoes.
In a bowl toss asparagus with 1 1/2 tablespoons olive oil, the remaining 2 cloves minced garlic, and 1/4 teaspoon salt and 1/4 teaspoon pepper. Arrange the asparagus around the potatoes and tomatoes. Slide the pan into the oven and bake until the chicken is cooked through and asparagus is tender-crisp, about 12–15 minutes.
Remove the pan and top each chicken piece with slices or torn pieces of mozzarella. Switch the oven to broil (high) and return the pan about 4–6 inches from the element just until the cheese melts and develops light golden spots, 2–3 minutes—watch carefully to prevent burning.
Take the pan out, drizzle everything with the balsamic glaze, scatter the torn basil over the top, and let the dish rest 2 minutes before serving so juices settle.