Mix the flour and paprika in a bowl. Add the butter and rub it in until the mixture resembles breadcrumbs. Add enough cold water to form a firm dough (just a couple of tablespoons). Turn out the dough onto a lightly floured surface and knead briefly. Chill for 30 minutes.
Preheat the oven to 200C/400F/gas mark 6. Roll out the pastry and line a 23cm pie dish. Chill the case for 30 minutes, then bake blind for 15 minutes. Remove from the oven and lower temperature to 180C/350F/gas mark 4.
Chop the peppers into small pieces and layer them over the bottom of the pie case. Cut the courgettes and carrots into ribbons and boil them for 2 minutes. Pat dry and lay over the peppers.
Beat the eggs, cheese and milk together and pour this over the vegetables. Bake for 35-40 minutes until the filling is set and golden brown.