Heat the oil in a large frying pan over high heat. Cook the mince, stirring with a wooden spoon to break up any lumps, for 10 minutes or until the mince changes colour. Add the tomato paste. Cook, stirring, for 1 minute to coat. Add the wine. Cook for 1 minute or until the wine evaporates. Add the pasta sauce, stock and oregano. Season. Simmer for 10 minutes or until reduced slightly.
Meanwhile, whisk the cream and eggs in a bowl until well combined. Season. Stir in 2 cups cheese.
Grease the insert of a 3.5L slow cooker. Spread a thin layer of the mince mixture over the base of the insert. Cover with a layer of lasagne sheets, breaking the sheets to fit, if necessary. Drizzle one-fifth of the cream mixture over the lasagne sheets and top with one-quarter of the remaining mince mixture. Continue layering with remaining lasagne sheets, cream mixture and mince mixture, finishing with a layer of cream mixture. Sprinkle with remaining 1 cup cheese.
Cook on Low for 3 1/2 – 4 hours or until the lasagne sheets are tender and the liquid is mostly absorbed. Carefully remove the insert from the slow cooker. Set aside, covered, for 10-15 minutes to rest. Sprinkle with parsley.
