Preheat oven to 350°F. Lightly grease a large casserole dish (about 12 inches long).
Set a large pan over medium heat and add the oil. When the oil is hot, add mushrooms, onions, and garlic and cook, stirring often, until onions soften and mushrooms release liquid.
Stir in tomato paste, savory, paprika, cumin, nutmeg, white pepper, and bouillon cube, if using. Fry for a little bit until mixture is well combined and fragrant, and tomato paste slightly changes in color.
Add potatoes and stir to coat them with the sauce. Add 1/4 cup water and stir. Cook potatoes until they are mostly cooked through, stirring occasionally so that they do not stick to the bottom. Season with salt and pepper.
Remove pan from the heat, add ground meat and stir to combine thoroughly. (You are not cooking the meat here, just combining it with the potatoes and seasonings.) Put the meat and potato mixture into the casserole dish and bake uncovered for 30 minutes until the meat is cooked. The top should be lightly browned and the meat should be solid like a meatloaf or burger patty. Drain the excess liquid and fat from the casserole dish, if necessary, and set aside.
In a bowl, beat together yogurt, flour, eggs, and baking soda. Season with salt and pepper lightly. Pour the yogurt mixture over the meat and potatoes and return to the oven. Bake for 15 minutes or until the top is golden and the yogurt is just set. (Do not overcook. The yogurt layer should be just firm enough so that it is not pure liquid. If you cook it too long, the yogurt will curdle.)
Let cool at room temperature for 10 minutes before serving.
I was born in Peru to a Limeño father and a Texan mother. We moved to Miami when I was five, and I grew up in the "Kendall-suyo" neighborhood—often called the 5th province of the Inca Empire because of its large Peruvian population. I've been writing about food since I was 11 years old, and in 2016 I received a master's degree in Gastronomy from Boston University. A travel columnist at Food52, I'm currently based in Hollywood, Florida—another vibrant Peruvian community—where I am a writer, culinary tour guide, and consultant.