To begin, bring a large pot of water to a gentle boil. Trim the tops and roots of the onions slightly, keeping them whole. Boil for 10 minutes to soften the outer layers. Drain and let cool slightly before peeling away layers. Move on to filling preparation.
Gently push the centres of the boiled onions out, leaving whole outer layers intact. Each layer will become a wrapper. Aim for 2 to 3 layers from each onion. Set aside and proceed to make the filling.
In a large bowl, combine minced beef, lamb, rinsed rice, egg, parsley, garlic, paprika, salt, and pepper. Use your hands to mix thoroughly until the ingredients form a uniform mixture. Prepare to stuff the onions.
Take one softened onion layer, hold it in your hand, and place a small amount of filling at the centre. Roll or fold it gently to enclose the mixture. Continue until all layers are filled. Move to arranging them in a pot.
Place the stuffed onions snugly in a wide, heavy bottomed pot. Layer them close together so they hold their shape during cooking. Transition to preparing the sauce.
In a separate bowl, whisk beef stock with tomato paste and flour until smooth. Pour the mixture over the onions in the pot. Dot the top with butter and add a bay leaf. Move to cooking.
Cover the pot and bring to a gentle simmer over medium heat. Lower to low heat and cook for 60 minutes. The onions will soften and the filling will cook evenly. Transition to finishing.
Once cooked, remove the lid and let the liquid reduce slightly if needed. Gently baste the onions with the sauce before removing from heat. Proceed to plating.
Transfer the Sogan Dolma to a serving dish. Spoon over the rich sauce and garnish with fresh parsley. Serve with thick yoghurt on the side and fresh bread to soak up the sauce.