Heat the olive oil either in a nonstick skillet or the bowl of your slow cooker, it it can go on the hob. Start by browning the beef very well. If you have a slow cooker with a bowl that can go directly on the hob, then you can do it all in one and you can skip the skillet.
Soften the onions and garlic and scrape up any little bits of beef in the bottom of the pan or slow cooker bowl. Add in the chopped mushrooms and carrots and continue to cook until the mushrooms are turning golden. About 5 minutes.
Place everything from the pan into the slow cooker, or if you've sauteed everything in the slow cooker add in the tomato puree, flour, red wine, Worcestershire sauce and beef stock. Cook the cottage pie filling on high for 3 hours, or low for 6-8 hours. In the last 30 minutes of cooking time, add in the handful of frozen peas.
While the cottage pie is cooking make the potatoes. Peel and chop the potatoes and place in a large pan of cold water and season well with salt. Bring the pan to a boil and cook uncovered until the potatoes are tender and cooked through. Drain them and mash with a potato masher. Add in the butter and Greek yoghurt if you’re using it. Pour in the milk in a steady stream and continue to mix until the potatoes are light and fluffy.
Once the filling is cooked, have a taste and check for seasoning. Add in anything you think it may need. Extra salt, pepper or thyme. Maybe a splash of water, if your gravy is really thick. While the beef is in the slow cooker make the mashed potato.
Scoop the filling into an ovenproof skillet or pie dish and spoon the mashed potato on top. For extra crispy potatoes, drag a fork across the top of the potatoes and top with some extra butter. Place under the grill for about 10 minutes or until the potatoes are golden and the tips of the potato mountains are crispy.