Put 2 tbsp of oil into a large skillet and place over medium heat. Add onions and 1/2 tsp salt and cook for 7-8 minutes, stirring often until golden brown.
Add the garlic, spices and tomato paste and cook for an additional minute. Stir in the plum tomatoes and cook for 5 minutes, until they've completely broken down and the mixture has thickened. Remove from heat and let cool.
Transfer the mix to a a medium bowl along with minced beef, cilantro, 1 tsp salt and black pepper to taste. Mix well and set aside.
Preheat oven to 400 F. Line a baking sheet with parchment paper.
Using a serrated knife, cut the pitas in half and fill each pocket with about 1/4 cup of the meat mixture, flattening it out so it fills the pita evenly.
Put 1 1/2 tsp butter and 1 tbsp oil in a large skillet and place over medium high heat or a grill. Add two of the sandwiches and cook for 3 minutes, flipping after a minute, until both sides have browned.
Transfer to prepared baking sheet. Continue process with remaining sandwiches.
Once they are all pan-fried, transfer the baking sheet to the oven and bake for 7 minutes. Remove from the oven and set aside to cool for 5 minutes.
Serve warm with lemon wedges and tahini sauce.