Preheat oven to 375°F.
Place puff pastry onto parchment-lined baking sheet and prick surface all over with fork.
Fold edges over slightly to form crust all around, pressing with fork slightly to seal. Brush with egg wash and bake for 6 minutes to lightly golden brown.
Remove from oven and sprinkle cheese over puff pastry.
Place sliced potatoes over cheese, followed by sausage pieces, making sure to leave 2 open areas to hold eggs.
Carefully crack eggs onto tart and top with rosemary leaves. Season with salt and cracked pepper and drizzle lightly with olive oil.
Bake tart for 8 to 10 minutes, or until puff pastry is golden brown and egg whites are set.