Preheat the oven to 425 degrees F.
Heat the butter in a saucepan over medium-low heat. Add in the shallots and garlic, cooking until soft and slightly golden, stirring occasionally, about 8 to 10 minutes. Stir in the tomato paste and cook for another 5 minutes. Add in the tomatoes, sherry, chicken stock, brown sugar, basil, salt and pepper, then bring the mixture to a boil. Reduce to a simmer and cook for 20 minutes.
Transfer the soup to a high-powered blender and carefully blend until pureed. Transfer back to the pot over low heat. Stir in the heavy cream. Taste and season additionally with salt and pepper if needed – it might, depending on your tomatoes.
Place 4 ramekins on a baking sheet. Use one of the ramekins to cut rounds in the sheet of puff pastry - you want 4 of them.
Ladle the tomato soup evenly into the ramekins. I like to use the larger ramekins that hold about 6 ounces in capacity.
Sprinkle about ¼ cup grated cheese on top of the soup. Top with a round of the puff pastry. Brush the pastry with egg wash then sprinkle with 1 to 2 more tablespoons of cheese. Repeat with remaining ramekins.
Bake for 20 to 25 minutes, until the puff pastry is golden and puffed and cooked through. Serve with a sprinkling of chives.