A classic Middle Eastern dish, Sini Kofte (Turkish) or Kibbeh bil Sanieh (Lebanese) is a layered, baked kofte. It features a beef and bulgur mixture as the base and topping, and a cooked ground beef mixture as the filling. It's considerably easy to make, and is excellent for entertaining guests, as it can be made ahead and reheated.
Start by making the gheyma (ground beef). Heat the butter in a medium skillet over medium-high heat. When melted add the ground beef, stirring and breaking up into small pieces. When the beef has started to brown but is not completely cooked yet, add the onions and season with salt, pepper, and paprika. Continue to cook until the beef is well-browned and cooked through. Taste and adjust seasoning as desired. Stir in the parsley and remove from the heat. The gheyma can be made ahead and reheated as needed. It can also be frozen.
Place the peeled, diced potato in a small saucepan filled with cold water. Heat over medium-high heat, bring to a boil, reduce the heat and simmer until tender. Drain any excess water and mash. Set aside.
Meanwhile, place the bulgur in a large mixing bowl. Soak the bulgur with 1 cup water (or more as needed) for about 15 to 20 minutes, or until softened (you can add a bit more water at a time until the bulgur absorbs it all). Mix in the ground beef, cornstarch, egg, and season with salt, pepper, and paprika by hand. Then add the mashed potato and combine until smooth. Wet hands as needed to ease mixing.
Preheat the oven to 375°F, with the rack set in the middle of the oven.
Lightly grease a 13-by-9-inch baking pan with olive oil. Divide the beef and bulgur mixture in half. Take large handfuls of the mixture and press them into the bottom of the pan creating an even layer to cover the entire pan (again, wetting hands will make this process much easier). Spread the gheyma evenly over the beef and bulgur layer.
Next, take large handfuls of the remainder of the beef and bulgur mixture and press them between your palms to flatten them to the same thickness you had beneath the gheyma, wetting hands between each frequently. Arrange these flattened discs of meat/bulgur over the gheyma evenly, patching them together to create a solid layer, filling in gaps with smaller flattened pieces as needed.
Cut into squares about 2 to 2 ½ inches across (alternatively you may cut diamonds), wiping down the knife in between cuts (wetting and wiping the knife helps clean it between cuts). After cutting the entire pan into squares, pour the oil evenly over the top. Next, pour the water over the top.
Bake, uncovered, for about 45 to 50 minutes, or until it is cooked through and the surface has lightly browned.
Use a knife to cut around the edges of the pan, and in between the squares. Serve hot or at room temperature with lemon wedges for squeezing.
You may also use the same type of ground beef for the beef and bulgur mixture as you would for ishli kofte or chi kofte (very fresh top round ground 3 to 4 times until paste-like). Many Armenians use this special ground beef for sini kofte. It's very lean and bright red. It yields a more firm and dense exterior to the sini kofte than if you use standard ground beef. It's also a brighter red color, very similar to the appearance and flavor of ishli kofte. My family has made it with both types of beef. Regular ground beef is a lot easier to source, and yields delicious results so we use that more often than the specially ground variety of beef.
You may also cut sini kofte into diamond shapes instead of squares. This is more traditional, but you will have some odd-shaped edge pieces. Cutting it into squares is more resourceful and yields uniform pieces. We usually do it that way, but you can try either shape.
Sini kofte can be made in advance and reheats very well. Arrange squares on a baking sheet, and reheat at 375°F until heated through.