Place the slices of baguette on a baking tray lined with baking paper. Toast for approx. 5 mins. each in the centre of an oven preheated to 220°C. Remove the tray, drizzle the bread with wine and top with the cheese, bake for a further 10 mins.
Heat the butter in a non-stick frying pan. Carefully slide each egg into the frying pan, fry for approx. 5 mins. over a low heat, season. Plate up the Valais cheese toasties, top with the fried eggs, serve.