Preheat oven to 350˚F. Line a 9”x13”, rimmed sheet pan with parchment and set aside.
Place a large skillet over medium heat and add 1 tablespoon oil. Once oil is hot add ground lamb and saute, breaking up with a wooden spoon. Add tomato paste, 2 tablespoons water, cumin, coriander, paprika, and ginger and season with salt and pepper. Continue to saute until tomato paste and spices have been evenly incorporate and the lamb has just browned. Transfer mixture to a plate and place skillet back over medium heat.
Add remaining oil to skillet followed by garlic and onion. Saute mixture until onions become slightly translucent, 6 to 7 minutes.
Add ground lamb mixture back to skillet and stir together with garlic and onions. Lightly season with salt and pepper, stir together and remove from heat.
Brush butter onto parchment and layer 5 sheets of phyllo dough into baking pan, brushing butter between each layer.
Sprinkle ¼ cup crushed nuts over the fifth layer of phyllo and top with half gruyere cheese. Evenly spoon half ground lamb mixture over the shredded gruyere and top with half of the Parmesan.
Top lamb and cheese mixture with 5 more sheets of phyllo, brushing butter between each layer.
Repeat steps 6 and 7 with remaining nuts, cheese and lamb mixture and finish baklava with remaining 5 sheets of phyllo, brushing butter between each layer. Cut 1 inch strips into baklava, in a diagonal pattern each way, creating diamond shaped pieces. Sprinkle some crushed pistachios and grated Parmesan over the top and bake for about 30 to 35 minutes or until golden brown.
Remove baklava from oven and cool for 10 to 15 minutes. Serve.