Preheat the oven to 350° (or 325° if the Bundt pan has a darker interior).
Roughly chop or tear the almond paste into a food processor and pulse a few times to break it up into slightly smaller bits—about 5 – 6 pulses. Sprinkle in the sugar, and pulse until the almond paste is totally finely ground into the sugar.
Sift together the baking soda, baking powder, salt, and all but a heaped spoonful of the flour (about 2 tablespoons, more or less) into a large measuring bowl and set aside.
In a stand-up mixer with the paddle attachment, cream the butter and shortening together just to combine—about 15 seconds—and then add in the golden, almond-perfumed sugar. Beat on medium speed for exactly 3 minutes until it’s a pale, almost ivory white, and fluffy. Scrape down the sides and bottom with a rubber spatula.
Turn the mixer down to medium-low, and add the eggs one at a time, allowing each one to incorporate almost completely before adding the next. In total, this whole process should take just about 30 seconds—you don’t want to beat the eggs too much because it can incorporate too much air, which could cause the cake to rise dramatically when baking (and, in turn, fall dramatically when cooling) or create air pockets in the cake, causing it to bake unevenly. Scrape the sides and bottom down again.
Once all the eggs are in, splash in the vanilla and, with the mixer on low, add a third of the dry mix. Let it mix in almost completely before adding a third of the sour cream. Allow the sour cream to incorporate before repeating the process twice more, using up all the dry mix and sour cream.
Toss the pitted and quartered cherries with the reserved heaping spoonful of flour in a bowl until the glistening crimson of the cherries is matted with white. Fold these into the batter with a rubber spatula with as quickly and with as little stirring as possible as not to toughen the cake, being sure to scrape the bottom of the bowl while you do.
Grease the pan with butter and dust with a little flour, knocking out all the excess. Add the batter into the pan, and smoothing out the top with the spatula. Don’t be alarmed—it is a very thick batter.
Bake for 45 – 55 minutes, until cooked through (a tooth pick should come out clean). If you’re using a pan with a dark interior keep a close watch on the cake—you’ll want to take it out closer to the 40 – 50 minute mark. Once it comes out of the oven it will continue to cook in the pan, even more so with a darker pan, so if the cake is removed when it’s perfectly baked it will dry out as it cools. For me and my darker pan, 45 - 50 minutes is the magic number here; I lightly touch the surface with my finger and it feels like it could use another 5 minutes, and that’s when I know it’s time to come out.
Allow it cool outside of the oven for about 15-20 minutes before inverting onto a wire cooling wrack. Let the cake cool completely—at least an hour—before adding any glaze/icing.
Top with some reserved cherries and/or slivered almonds as you see fit. This cake is best enjoyed within 2 – 3 days and stored at room temperature (and because there’s no milk in the glaze, it doesn’t need to be refrigerated).
To make the glazes:
To make the glazes, whisk the sifted powdered sugar with their respective liquids until you have a smooth glaze. For the amaretto glaze, whisk the sifted powdered sugar, amaretto, vanilla extract, and melted butter to combine before adding just enough water to make it a thick, but still pourable, glaze. If you’re unsure, spoon a little over a portion of the cake to make sure it’s thick enough to stick—if it’s too thin just add a little more powdered sugar. To make the cherry glaze, similarly add cherry juice to the powdered sugar until you have a smooth glaze—this one can be slightly thinner. You can spoon, pour, or pipe—anyway you like.
If you want little bits of cherries to run throughout the cake, chop them a bit smaller—let’s say into eighths, roughly, rather than quartering them—and then toss with flour. I prefer to keep them quartered; it means you get big pops of juicy cherries rather than the cake being flecked with little specks of fruit.
Don't feel inclined to make both glazes, though they're both so good. One will do if you like.