Line a baking sheet with parchment paper. Cut cheese in half to create 2 flat discs and then cut each disc into 8 wedges. Place wedges on prepared baking sheet and freeze, 1 hour.
Preheat oven to 350°F (180°C). Prepare tempura batter according to package directions and season with salt and pepper. Pour panko into a bowl. Dip each piece of cheese into tempura batter and then into panko, coating evenly. Heat a large saucepan filled with 1 in. (1 cm) of oil over medium-high heat until a candy thermometer reads 375°F (190°C). Working in batches, carefully drop panko-coated cheese into hot oil and fry until golden brown, about 2 min. per side. Using tongs, remove cheese from oil and place on a paper towel–lined plate. Transfer cheese back onto baking sheet and bake on middle rack of oven until cheese starts to bubble out of the crust, 3 to 5 min.
Heat butter in a small saucepan over medium heat. Add onions and cook until softened, about 2 min. Add sugar and vinegar and cook, stirring, until sugar dissolves and vinegar starts to boil, about 3 min. Add tomatoes and remaining salt and pepper, reduce heat to medium-low and cook, stirring often, until juices have evaporated completely, about 20 min. Stir in fresh basil. Top each piece of cheese with tomato confit and serve.
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