Preheat oven to 400°F (200°C). Toss the cherry tomatoes with 1/2 tablespoon of olive oil, salt, and pepper. Roast for 10-15 minutes until blistered.
Spiralize the zucchini. Place the noodles in a colander, sprinkle lightly with salt, and let sit for 10 minutes to release excess moisture. Pat completely dry with paper towels.
Heat the remaining 1/2 tablespoon of olive oil in a large skillet over medium-high heat. Add the zucchini noodles and sauté for 1 to 2 minutes until just warmed through. Do not overcook.
Remove the skillet from heat. Add the pesto sauce and gently toss to coat the noodles evenly.
Divide among plates. Top with roasted cherry tomatoes, grated Parmesan cheese, and fresh chopped basil before serving.