Cut blemished parts off of tomatoes. Crush tomatoes with your hands over a bowl to remove as much of the seeds as possible, until you have 6 cups of crushed tomatoes.
Add olive oil to the slow cooker, stir in all the crushed tomatoes, chopped onions, garlic, shredded carrot, parsley, and sugar. Cover and simmer on low for 8 hours. Let cool and refrigerate overnight.
Puree to desired consistency using an immersion blender or in batch in a stand blender. Reheat on the stove over medium-low heat until hot.