Preheat the oven to 325 degrees F (165 degrees C). Butter a 10-inch tube pan and cover with sugar.

Mix 2 cups sugar and 1 cup butter together using an electric mixer in a large bowl until fluffy. Add eggs one at a time, making sure they are well incorporated. Stir in vanilla extract.

Whisk 2 3/4 cups flour, baking powder, and salt together in a medium bowl. Stir flour mixture gradually into the butter mixture until combined.

Coat peaches in remaining 1/4 cup flour; fold into the batter. Pour batter into the prepared pan.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 1 hour to 1 hour 10 minutes. Remove from the oven and let cool for 10 minutes before flipping cake onto a wire cooling rack to cool completely.