1
Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce the heat to medium-low and simmer until tender, about 20 minutes.
2
While the potatoes are cooking, heat oil in a large skillet over medium heat. Add onion; cook and stir until translucent, about 5 minutes, adding garlic for the last minute. Stir in diced tomatoes and tomato paste; cook until tomatoes soften and begin to lose their shape, 3 to 5 minutes.
3
Add ground beef to the skillet; cook and stir until browned and crumbly, about 10 minutes. Stir in Panquehue cheese, parsley, and cayenne pepper; season with salt and pepper. Turn off the heat and let sit until needed.
4
Preheat the oven to 350 degrees F (175 degrees C). Grease a 2-quart baking dish.
5
Drain potatoes in a colander, then allow to steam dry for 1 to 2 minutes. Transfer potatoes back to the pot, add butter and salt, and mash until smooth. Let cool until just warm, 5 to 10 minutes, then stir in beaten egg.
6
Spread 1/2 of the mashed potatoes over the bottom of the prepared baking dish. Layer ground beef mixture over top, then completely cover with remaining potatoes.
7
Bake in the preheated oven until potatoes are hot and lightly browned on top, about 40 minutes.