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.
Halved the recipe since there was just my husband and I. Only problem I had was that the batter "broke" when I added the peach/buttermilk to the butter, sugar & eggs. Added the flour anyway and put the whole ugly mixture (lumpy - looked curdled, but wasn't) in the baking pan. After all that effort I wasn't about to throw it out without at least trying to cook it.
Came out fine!! More than fine - it was absolutely delicious. Husband had 2 helpings and I'm considering a 2nd.
I think that my batter broke because my butter/sugar mixture never got real fluffy - probably the butter wasn't soft enough, If it happens to you - carry on anyway. You won't be disappointed.