Arrange tomatoes, flesh side up, on 2 wire racks set on sheet trays. Drizzle the tomatoes with olive oil, making sure they are well covered. Season with salt, pepper and sugar.
Roast in the middle rack of the oven until tomatoes are brown and tender, about 1 hour. Cool slightly.
Melt butter in 4-quart saucepan over medium heat. Saute the shallots for 2 minutes, and then mix in tomato paste for a few more minutes. Add chicken stock and cayenne. Add heavy cream and heat over low heat. Bring up to a boil then reduce heat to low and let simmer for 10 minutes. Add the roasted tomatoes to the pan.
Puree with an immersion blender. Season with salt and pepper. Ladle into serving bowls and garnish generously with fresh basil.