Preheat the oven to 425 and lightly grease a rimmed baking sheet.
Open cans of whole tomatoes and drain off the juice. Place tomatoes in the cookie sheet, in one even layer. Drizzle with some olive oil and sprinkle some oregano over tomatoes.
Bake for 15-18 minutes.
Meanwhile, preheat a pot on stovetop over medium heat.
Add some oil for cooking and add diced onion and carrots.
Peel, smash, and chop garlic. Add it to the veggies. Sautee for a few minutes.
Add roasted tomatoes to the pot and mix well.
Sprinkle flour over veggies evenly and mix well.
Start pouring in broth, while stirring.
Add salt, sugar, and basil. Stir and cook for about 15 minutes.
Blend everything until smooth. You can use an immersion blender to blend everything smooth or you can transfer it into a standing blender.
If using a stand up mixer, transfer blended soup back into the pot. Stir in heavy whipping cream.
Add gnocchi and cook until they start to float up.
**If serving all the soup right away, cook all the gnocchi in the soup. If you only plan to eat a couple of servings at first, cook a portion of gnocchi in soup as needed. If you leave gnocchi in liquid for too long, it will get too mushy, much like pasta.