In a large soup pot over high heat, melt the butter then combine the crushed tomatoes, cherry tomatoes, shallot and garlic. Season with red pepper flakes, salt and pepper, to taste. Saute until some of the moisture has been released - about 15 minutes, stirring to prevent any sticking.
Deglaze the pot with the wine and scrape up any browned bits on the bottom of the pot. Add the chicken broth. Cover and bring the pot to a simmer for about 30 minutes, stirring occasionally.
Use an immersion blender to blend the soup until smooth (or your desired level of chunkiness). Alternatively, transfer the soup to a blender and blend until smooth - do not overfill the blender, work in batches if using this method. Return the soup to the pot. If you prefer a chunkier soup, skip blending.
Add the gnocchi and cook for 5-8 minutes (or according to the instructions on the package). Stir in the grated Parmesan, heavy cream, basil and goat cheese. Continue to stir until the goat cheese is melted. Season with salt and pepper, to taste. Enjoy!