Heat oven to 220C/200C fan/gas 7. Wrap the whole courgettes in foil, then put in the oven and roast for 20 mins or until soft when pricked with a fork. Remove from the oven and allow to cool completely.
Put the courgettes in a food processor, with the garlic and blend until it has a fluffy texture. Add the tahini and lemon juice and season, then blitz again. Transfer to a bowl, then stir through the yogurt and a little of the mint. Drizzle with olive oil and scatter over the remaining mint to serve.