Preheat the slow cooker if necessary; see the manufacturer's instructions. Line the grill rack with foil. Arrange all the vegetables on the foil in a single layer, with the peppers skin side up. Drizzle with the oil and sprinkle with the garlic and salt and pepper. Grill for 10 minutes or until softened and browned. Transfer the courgette slices to a plate and wrap the peppers in the foil. Leave to stand for 5 minutes to loosen the skins.
Oil a 500 g (1 lb) loaf tin and line the base and two long sides with nonstick baking paper, checking first it will fit in the slow cooker pot. Beat together the eggs, milk, Parmesan, basil and salt and pepper in a bowl. Unwrap the peppers, peel away the skins with a knife.
Arrange one-third of the courgette slices over the base of the tin. Spoon in a little of the custard, then add the peppers and a little more custard. Repeat, ending with a layer of courgettes and custard. Cover the top with foil and put in the slow cooker pot. Pour boiling water into the pot to come halfway up the sides of the tin. Cover with the lid and cook on high for 2–3 hours or until the custard is set.
Lift out the tin using a tea towel and leave to cool. Loosen the edges with a knife, turn out on to a chopping board and peel off the lining paper. Cut into slices and serve with romseco sauce (see below).