In a medium pot, heat the EVOO over medium-high. Melt 2 tbsp. butter into the oil, then add the onions, garlic, thyme and paprika; season with salt and pepper. Partially cover the pot and cook until the onions and garlic are softened, 10 minutes. Stir in the tomato paste; continue stirring until fragrant, 2 minutes. Deglaze the pan with 2 cups stock. Transfer the mixture to a food processor, add the tomatoes and process until smooth. Pour the soup back into the pot and add the remaining 2 cups stock; reduce heat and simmer while you make the grilled cheese.
Preheat a griddle or grill pan over medium heat. Sandwich 2 slices of cheese between 2 slices of bread, then spread the outsides of both bread slices with softened butter. Repeat with the remaining cheese and bread. Grill, turning once, until the bread is crispy and the cheese melts.
Stir the cream into the soup. Divide the soup among bowls, sprinkle with chives and serve with grilled cheese for dipping.