Heat the olive oil in a large saute pan or wide pot over medium-high heat. Add the onion and cook for 4-5 minutes until softened. Add the garlic and cook 1 minute more. Add the ground meat, breaking it apart with a wooden spoon. Cook over medium-high heat, stirring frequently, until the meat is fully browned and all the liquid has evaporated, about 10-12 minutes. The meat should be sizzling and beginning to caramelize, not steaming in liquid.
If using wine, add it now and let it bubble and evaporate for 1-2 minutes. Add the cinnamon, allspice, and bay leaves and stir to coat the meat in the spices. The cinnamon aroma should bloom immediately.
Add the crushed tomatoes and tomato paste. Stir to combine. Reduce heat to medium-low and simmer, stirring occasionally, for 15-20 minutes until the sauce has thickened and the meat is no longer sitting in liquid. The kima is ready when a wooden spoon dragged across the bottom of the pan leaves a clean line that fills in slowly. Season well with salt and black pepper. Remove the bay leaves.
While the sauce simmers, bring a large pot of well-salted water to a boil. Cook the pasta according to package instructions until al dente. Reserve 1/2 cup of pasta cooking water before draining.
Drain the pasta and plate immediately. Spoon a generous amount of kima over the pasta, grate the cheese heavily over the top, and serve. Each person mixes their own at the table.