Equipment and preparation: You will need a commercial ice cream maker or sorbetier.
For the basil sorbet, place the sugar and water into a pan and place over a low heat, stirring occasionally, until dissolved. Stir in the basil until wilted and the squeeze o flemon juice. Transfer the mixture to a food processor and blend until smooth.
Pass the mixture through a fine sieve into a second sieve lined with muslin cloth and set over a bowl. Set aside to drain and cool.
Pour the strained mixture into an ice cream machine and churn according to the manufacturer's instructons. Meanwhile, line a baking sheet with non-stick baking paper.
When the sorbet is ready, use 2 spoons to shape quenelles and place them onto the lined tray. Freeze until ready to serve. (Any remaining sorbet can be scooped into a freeze-proof container and kept in the freezer.) Take the sorbet out of the freezer about 10 minutes before serving to allow them to soften.
Preheat the oven to 200C/400F/gas 6. Line 2 baking sheets with non-stick baking parchment and grease the outsides of 6-8 dariole moulds, sitting half of them upside down on another baking sheet.
For the tuille baskets, crush the garlic, then mince to a fine paste with the salt crystals using the back of a knife. Beat the butter in a bowl until pale and creamy, then mix in the flour, sugar and garlic paste. Slowly mix in the egg white and grated parmesan to form a sticky paste.
Place 3-4 spoonfuls of the mixture onto one of the prepared baking sheet and spread each one out into a 12cm/6in round with a palette knife. Sprinkle over some rosemary leaves and bake for 6-8 minutes, or until the rounds are golden-brown around the edges but still pale in the middle.
Remove the cheese rounds from the oven. Working carefully and quickly, use a palette knife to drape them over the upturned dariole moulds, shaping the rounds around them. Place back into the oven for 3-4 minutes, or until golden-brown. Remove and set aside to cool for a few seconds before removing the 'baskets' from the moulds. Set aside to cool on a wire rack. Repeat with the remaining mixture to make enough baskets for serving, using the remaining greased dariole moulds (this recipe will yield a maximum of 8 baskets to allow for breakages).
For the basil oil, blend the basil leaves with the olive oil in a food processor, then strain through a fine sieve set over a bowl. Set aside to drain.
For the tomatoes, place all of the tomatoes into a large bowl and cover with boiling water. Scoop out the cherry tomatoes after 30 seconds and the larger tomatoes after one minute. Carefully peel away their skins.
Place the cherry tomatoes into a bowl and season with salt and a splash of olive oil.
Halve and de-seed the tomatoes and place into a bowl. Add a splash of olive oil and the balsamic vinegar and season well with salt and freshly ground black pepper. Mix well.
To serve, place a tuille basket onto each plate and divide the cherry tomatoes among them. Place a quenelle of basil sorbet on top. Spoon the dressed tomatoes alongside and drizzle the basil oil around the plate.
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