Preheat oven to 350º. Sift together first 7 ingredients; sift again.
Process chopped peaches in a food processor or blender until smooth. (Yield should be 2 cups puree.) Stir in buttermilk.
Beat butter and sugar at high speed with a heavy-duty electric stand mixer until fluffy. Add eggs, 1 at a time, beating until blended after each addition. Add peach mixture, and beat until well blended.
Layer sliced peaches in a greased 13- x 9-inch pan.
Fold flour mixture into butter mixture. Pour batter over sliced peaches in pan. Place pan in a large roasting pan, and add boiling water to roasting pan to a depth of 1 inch.
Bake at 350º for 50 minutes or until set. (Pudding will still be moist.) Serve warm or cold with ice cream.