Peel and thinly slice the onions. Place in a large pot over a medium heat with the oil, butter and a really generous pinch of salt.
Cook the onions, stirring frequently, for about 10-15 minutes until they have softened. Turn the heat down to low, and keep cooking for a further 30-45 minutes. If you are worried that the onions are beginning to 'catch'/burn, add more oil or butter.
Once the onions are a gorgeous brown color, add a few teaspoons of fresh thyme leaves, some cracked black pepper and the beef broth. Keep cooking until most of the beef broth has cooked down, so there isn't a lot of liquid remaining. Once done, turn the heat off while prepping the crust.
Preheat the oven to 400℉/200℃. Line 1-2 large baking trays.
Roll out the pastry crust to about 1/4 inch thick. Cut into about 7-8 inch diameter circles (use a plate to create a perfect circle). Place one disc onto the baking tray and sprinkle with flour. Top with half the onion mixture.
Fold the crust over the filling, like the photos. Repeat for the other galette. Brush the crust with beaten egg.
Bake about 20-25 minutes, until the crust is golden. Remove and serve warm, topped with extra fresh thyme for decoration!