Preheat the oven to 200°C/390° F in convection mode.
Place the vegetables (tomatoes, onion) along with the garlic in a baking pan, sprinkle with olive oil, salt and pepper, and bake in the oven for 30 minutes.
Transfer the vegetables to a bowl, add the butter, and blend with a hand blender until puréed.
Boil the gnocchi in salted water for 4 minutes. Strain when cooked. With a slotted spoon, transfer them to the bowl of water and ice and leave them until they cool. Transferring the gnocchi to iced water stops the gnocchi from overcooking and falling apart.
Heat a large pan over medium to high heat, add in the puréed vegetables along with the heavy cream. Simmer for 4-5 minutes and, as soon as the sauce thickens, add the gnocchi. Cook for 1 minute, turn off the heat and add the mozzarella cheese.
Sprinkle with fresh basil, season with salt and pepper, stir gently and serve.