Preheat the oven to 400°F.
Add the cherry tomatoes to an oven-safe dish. Drizzle with 2 tbsp. olive oil and salt to taste.
In a separate oven-safe dish or baking sheet, add the zucchini and sprinkle the minced garlic, 2 tbsp. olive oil, salt and red chili flakes over top.
Roast both the tomatoes and zucchini in the oven for about 20-30 minutes until soft.
Meanwhile, bring a large pot of water to a boil.
When the roasted tomatoes and zucchini are done cooking, remove from the oven. Set the tomatoes aside.
Add the roasted zucchini to a blender along with the remaining ingredients. Blend until smooth. Add more salt to taste.
Once the water comes to a boil, add plenty of salt. Cook the pasta until it's al dente. Reserve 1 cup of pasta water.
Strain the pasta and add to a large sauté pan along with the zucchini cream and ¼ cup of pasta water. Toss over medium-low heat.
Stir in the Parmigiano and toss again, adding more pasta water as needed.
Plate and top with the roasted cherry tomatoes, burrata and basil.
