For the Pesto:Wash and dry the fresh basil and blend it together with the other pesto ingredients in a food processor. For more tips and details, visit my post for Classic Pesto.
For the Soup:In a large stock pot, melt the butter.
Add diced celery and onions. Cook until translucent. Transfer to a 6-quart or 8-quart slow cooker. (I had to split mine into a 2-quart and 4-quart slow cooker since that's all I had.)
Add the pesto, whole tomatoes with juices, and dried oregano. Cook on low for 8 to 10 hours or high for 4 to 6 hours.
Using an immersion blender, blend soup until smooth. Stir in half & half and let it heat through, another 15 to 30 minutes, or serve immediately as is. Add salt to taste, if needed.