Preheat the oven to 220ºC fan.
Pour the oil into a large roasting tin and set it on the middle shelf of the oven to heat for a few minutes. Put the sprouts in the roasting tin, cut-side down, season with a pinch of salt and roast for 20 minutes until deeply charred and beginning to soften.
Stir in the kale and return to the oven for 6 to 7 minutes. (Depending on the size of your tray, you may need to use two trays to make sure they are not overcrowded and the greens crisp up nicely.)
Meanwhile, to make the sauce, heat the olive oil in a small saucepan over a medium heat, add the peanuts and cook for 2 to 3 minutes until golden. Remove from the heat and add the garlic and sesame seeds. Let everything bubble up for 1 minute then stir in the remaining ingredients. Keep stirring until the sugar has dissolved, then pour into a bowl and leave to cool.
Pour the sauce over the vegetables, toss to coat, then spoon into bowls and serve.
Substitutions: Sherry vinegar: apple cider vinegar or balsamic vinegar.
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