In a medium stockpot or Dutch oven, melt butter with 1 tablespoon oil over medium heat. Add bread; cook, stirring occasionally, until golden brown, 4 to 5 minutes. Remove bread from pot.
In same pot, heat remaining 1 tablespoon oil over medium heat. Add onion and garlic; cook, stirring occasionally, until translucent and aromatic, 5 to 7 minutes. Increase heat to medium-high. Add peeled tomatoes and broth; bring to a gentle boil. Reduce heat to medium-low, and simmer, stirring occasionally, for 15 minutes. Add 2 cups toasted bread and oregano, stirring until combined. Cook, stirring occasionally, until bread is softened, 10 to 15 minutes. Using an immersion blender, carefully blend until smooth.
In a small bowl, combine sour cream and mayonnaise, stirring until smooth.
To serve, top servings of soup with sour cream mixture, remaining toasted bread, and diced tomato. Garnish with oregano, if desired.
Recipe by Paula Deen Magazine at https://pauladeenmagazine.com/tomato-sandwich-soup/