Preheat oven to 350°F. Wrap a 12x12-inch square of parchment paper over the metal bottom of a 9- or 10-inch springform pan. (Springform pans usually are flat on one side with a lip on the other—put the flat side up, even though it seems upside down.) Clamp the parchment inside the metal ring with the pan bottom; the parchment will become an easy-to-remove lining. Brush the sides of the pan with melted butter, or line the sides with strips of parchment the height of the pan.
Beat butter until light and smooth. Rub sugar and orange zest together so the orange oil infuses the sugar.
Whisk the cornmeal with the baking powder, salt, cardamom, and cinnamon, until the spices are evenly dispersed. Set aside.
Beat the sugar into the butter until the mixture is light and aerated, about 5 minutes. While creaming the butter and sugar, stop and scrape the button and sides of the bowl twice.
On low speed, mix the almond flour into the creamed butter, until just combined. Remove from mixer and transfer to a large bowl. By hand, using a large rubber spatula, fold in the cornmeal mixture. Fold in the beaten eggs, orange juice, and carrots, until the batter is well-mixed.
Spread the batter into the prepared pan, smoothing the top. Bake 25 minutes, then lower the heat to 325°F, and bake for another 25 to 30 minutes, until the top of the cake is golden brown and springs back when touched with a finger.
Make the glaze while the cake is baking.
Mix the orange juice, lemon juice, honey and cinnamon stick, if using, in a stainless steel saucepan. Bring to a boil, then reduce the heat, and simmer until the glaze reduces and thickens into a light syrup. Remove the cinnamon stick and stir in the orange liqueur. Keep warm.
As soon as the cake comes out of the oven, use a toothpick to poke holes every inch or so, then pour the warm glaze over.
You can leave the cake on the springform bottom, or, very carefully, slide the cake off the parchment paper onto a serving platter. (The cake is moist and honey-sticky so you have to be super cautious when moving it.)
Let cool 2 to 4 hours. Every so often, tilt the pan to swirl the glaze over the top of the cake. When the cake is no longer warm, and the glaze has been absorbed into the cake, refrigerate for an hour, to make it easier to remove the cake from the pan. Run a knife around the edge of the pan and unclamp to remove the sides of the pan.