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Preheat the oven to 350°F (175°C).
Make the peach filling: In a saucepan, combine peaches, butter, both sugars, vanilla, cinnamon, nutmeg, orange juice, and cornstarch. Bring to a slow boil, stirring until it thickens. Remove from heat and cool.
Prepare the bundt pan: Butter and flour a large bundt cake pan.
Mix dry ingredients: In a bowl, whisk together flour, baking powder, cinnamon, and nutmeg.
Cream butter and sugar: In a mixer, beat butter and sugar until fluffy. Add eggs one at a time.
Add flavorings: Stir in vanilla and almond extract.
Combine wet and dry: Gradually alternate adding the dry mixture and milk to the batter. Do not overmix.
Layer the cake: Pour half the batter into the pan, spoon in most of the peach filling (reserve some for topping), then add remaining batter on top.
Bake: Bake for 1 hour and 15 minutes. Test with a toothpick; it should come out clean.
Cool and top: Let cool 30 minutes before turning the cake out onto a platter. Top with reserved peach filling.
Serving and Storage Tips:
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