Preheat the oven to 350 (F) and prepare a 9 x 5-inch loaf pan by spraying generously with cooking spray. Set aside.
In a small bowl, combine 1 1/2 cups granulated sugar and the fresh zest from 1 medium orange. Use your fingers to rub the zest into the sugar until it starts to form clumps; doing so will release oils from the orange that will infuse your sugar and make it more fragrant. Set aside.
In a medium bowl, combine 2 cups all-purpose flour, 1 teaspoon ground cinnamon, and 1 teaspoon kosher salt. Use a spice grinder to grind 5 to 6 cardamom pods into the mixture. To grind cardamom, remove the seeds from each cardamom pod by using the flat of a chef’s knife and pressing down firmly on the pod (in the same way you would smash a clove of garlic). Pry open the shell, pick out the cardamom seeds, and use the spice grinder to grind the seeds into a fine powder over the flour mixture. Whisk the spices into the flour until well combined. Set aside. In the bowl of a freestanding electric mixer fitted with a paddle attachment, beat 1 1/2 cups unsalted butter on medium-low speed until it becomes light and fluffy, about a minute. Add the sugar and the zest (from the 2nd step) and increase the mixer to medium-high, beating for an additional 3 to 5 minutes and scraping down the sides of the bowl as needed.
When the butter and sugar mixture is light, fluffy, and almost doubled in size, reduce the mixer speed to its lowest setting. Add 6 large eggs one at a time, only adding the next egg when the first one has fully incorporated into the batter. One all the eggs have been added, add 1 teaspoon orange extract and 1/2 teaspoon pure vanilla extract.
Scrape down the sides of the bowl and turn the mixer back on to its lowest setting, and add the flour mixture (from the 3rd step). Continue beating on low speed until the dry ingredients have just combined into the wet — it’s best to still have one or two flour streaks in the mixture and finish the mixing by hand with a rubber spatula.
Transfer the batter into the prepared pan, smoothing the batter evenly across the pan with an offset spatula. Bake in the preheated oven for 1 hour, or until the cake is golden with a signature split in the center of a loaf. A cake tester inserted into the center of the cake should come out clean with minimal crumbs. See baker's notes — if the edges begin to brown too much before the center is set, loosely cover the edges with a couple pieces of aluminum foil.
Once the cake is finished, transfer to a wire rack to cool for 10 to 15 minutes, before using a wooden skewer or fork to poke holes all over the cake. Use a pastry brush to spread the rum simple syrup across the cake, making sure that the syrup seeps into the holes that you just created. It will seem like there’s too much syrup, but just be patient — the cake will absorb the liquid. Be sure to use all of it for a delicious and incredibly moist cake. Continue to cool the cake on a wire rack until the cake is warm but not hot.