Line the bottom of a 9-inch springform pan with parchment paper. Set aside.
For the crust
Add the cookies to a food processor fitted with the blade attachment and blend until you have fine crumbs. (Shortbread cookies crush very easily, so if you don't have a food processor, you can put them in a heavy-duty zip-lock bag, seal it, and roll over it with a rolling pin, or pound gently with the bottom of a small sauté pan.) Add the cardamom, cinnamon, salt, tangerine zest and melted butter and blend until everything is evenly combined. Set aside.
For the filling
Add the softened cream cheese to a medium-sized mixing bowl and mix until it's very smooth without any lumps. Then mix in the sweetened condensed milk, lemon juice vanilla and tangerine zest. Stir until it's a creamy, smooth consistency and set aside.
Peel about 5 of the zested tangerines and cut them horizontally into thin slices, about ¼-inch thick.
Assembly
Line the bottom of the springform pan, on top of the parchment paper, with the tangerine slices. You can break some of the slices apart to fill in the smaller spaces.
Sprinkle about ½ cup of the crust mixture on top of the slices and gently spread it out to cover them. (It might not cover the tangerine slices 100%, which is perfectly okay.)
Pour the filling on top and gently spread it out evenly. Then top it with the remaining crust mixture, spreading it out evenly as well. Cover the pan with plastic wrap and place the pan in the refrigerator for at least 8 hours (ideally overnight).
Serving
To remove the cheesecake from the pan, invert it onto a very large plate or a serving platter. Press gently on the bottom piece of the pan to slide the cake down, then unlatch the spring.
Use a very sharp knife to cut the cake into slices.