Generously spread shortening in a 12-cup Bundt pan and dust with flour. Tap out the excess flour. Peel and dice 2-3 fresh peaches. Preheat your oven to 300°.
Whisk together the flour, salt, and baking soda in a small bowl.
In a large mixing bowl, beat the butter and sugar at medium speed for 3-4 minutes with an electric hand mixer. Beat the eggs in one at a time, occasionally scraping the sides of the bowl with a silicone spatula.
Add the dry ingredients and stir in just until combined.
Beat in the sour cream, almond extract, and vanilla, scraping the bottom of the bowl. The batter should be smooth. Fold in the diced peaches.
Spread the batter into the prepared Bundt pan. Bake at 300° for about 90 minutes, or until a cake tester or toothpick inserted in the middle comes out with no wet batter.
Let the cake cool in the pan for about 15 minutes, then carefully invert onto a cooling rack. Cool for 60-90 minutes.
Peach Icing
After the cake is cool, prepare the icing. Blend the diced peaches and cream in a food processor until very smooth. Set aside.
Melt the butter in a glass bowl. Add the powdered sugar, salt, almond extract, and vanilla. Beat in half of the peach puree, then add as much as needed to get a pourable consistency. Spread over the top of the cake and let it run down the sides.
Notes
To bring your eggs to room temperature quickly, you can place them in a bowl of very warm water for a few minutes.
If you don't have a way to puree the peaches for the icing, you can use orange juice instead.
Leftover cake can be stored in an airtight container for 3-4 days at room temperature. I love using this cake taker.