Preheat the oven to 170C/325F/Gas 3.
For the vegetables, line a baking tray with aluminium foil, place the peppers on the tray, drizzle with one tablespoon of the olive oil and season with salt and freshly ground black pepper. Roast in the oven for 20 minutes, then remove the peppers from the oven and leave to cool. Once cooled, peel and chop into strips.
Heat the remaining olive oil in a pan and fry the courgette and aubergine for a few minutes, seasoning with salt and freshly ground black pepper.
In a bowl, mix the peppers, courgettes and aubergines together with the chopped basil and balsamic vinegar.
Preheat a grill to medium.
For the toastie, brush the sliced bread with olive oil and toast the bread on both sides under the grill. Place a large spoonful of the vegetable mixture onto the toast and then top with goats' cheese. Return to the grill until the goats' cheese begins to melt and turn golden.