Preheat the oven to 350 degrees F. Grease a 10 to 15-cup capacity bundt or tube pan with butter or shortening. Then add a few tablespoons of sugar to the pan and shake it around to coat the pan on all sides.
Place the butter and sugar in the bowl of an electric stand mixer. Beat on high to the butter and sugar until very light and fluffy, about 5 minutes.
Scrape the bowl with a spatula, then turn the mixer on low and add the flour, salt, eggs, vanilla, and almond extract. Scrape the bowl again, then mix in the diced peaches and chopped green chiles, until smooth.
Scoop the cake batter into the prepared pan. Jiggle the pan a little to remove air bubbles. Bake undisturbed for 80 minutes. Then insert a wooden skewer into the center of the cake. If it comes out clean the cake is done. If it has batter on it, bake another 10 minutes.
Let the cake rest in the pan for 10 minutes before flipping it out onto a cake stand.