Preheat the oven to 200°C, fan 180°C, gas 6. Meanwhile, cook the courgettes whole in a large pan of boiling water for 5 minutes, drain, then leave to cool slightly. Halve the cooked courgettes lengthways and scoop out the flesh. Set aside the hollowed-out halves and roughly chop the cooked flesh.
Heat the oil in a large frying pan, add the chopped courgette flesh and garlic, and cook for 5 minutes, until golden. Transfer the mixture to a large bowl and mix in the grated carrot, breadcrumbs, raisins, beaten egg, basil, thyme and most of the grated cheddar.
Spoon the mixture back into the hollowed-out courgette halves and scatter the reserved grated cheddar over the top. Arrange the courgettes side-by-side in a large baking dish and bake in the oven for 20 minutes, until the tops are a lovely golden brown.