Preheat the oven to 350 degrees F (175 degrees C). Generously grease and lightly flour a 2-part 10-inch tube pan.
Combine flour, sugar, butter, and salt in a large bowl; stir with a fork or pastry knife to blend all ingredients. Measure 1 cup of the flour-butter mixture and set aside. Add baking powder and baking soda to the large bowl, and stir well.
Whisk buttermilk, egg, and vanilla together in a second bowl. Add wet ingredients to the flour mixture and stir, briskly, with a whisk, until mixture is very smooth and fluffy, about 3 minutes. Spoon batter into prepared pan, smoothing and leveling the top.
Warm peach preserves in the microwave or in a small pot and smash any large fruit pieces. Spoon warm preserves on top of the batter.
Combine reserved flour-butter mixture, chopped almonds, brown sugar, and cinnamon in a small bowl. Sprinkle crumbs evenly on top of the preserves.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 40 minutes.
Transfer pan to a rack and cool for about 10 minutes. Remove the outer part of the tube pan and continue cooling, about 10 minutes. Slide a knife around the bottom of the cake to loosen from the pan. Using a spatula in each hand, lift the cake from the tube portion of the pan and place on a serving plate. Serve warm.