Heat a griddle pan and toast the bread for about 2 mins on each side until golden and marked. Rub the cut side of the garlic clove over each piece.
Heat the butter in a large frying pan. Add the parsnips, season with sea salt and freshly ground black pepper, then cook over a medium heat, shaking regularly until golden and softened, about 20 mins. Add a splash of water if you need to. Remove from the heat and whizz to a purée in a food processor with both of the oils. Season to taste. Set aside at room temperature if serving on the day. Can be chilled up to two days ahead.
To serve, top the toasts with the truffled parsnip mix (it should be room temperature), scatter with rocket leaves and parmesan shavings, then drizzle with a little more olive oil or truffle oil.