Preheat oven to 350 degrees F/175 degrees C. Grease and flour a 9x13 inch pan.
In a large mixing bowl, add the sugar, melted butter, eggs, and vanilla. Whisk until well-combined.
Alternately fold in the sifted flour, peaches, and walnuts until well-combined. Pour into the prepared pan, and smooth out the batter so it’s evenly distributed.
Bake 35-40 minutes, or until the edges are golden brown and a toothpick inserted in the center comes out clean.
Cool, slice, and serve. (Refrigerate for 30 minutes for easier slicing.) Dust with powdered sugar if desired.
A note on peeling peaches: Score the bottom of each peach with an "X" using a paring knife. Blanch them in boiling water for 40-60 seconds (less time for really ripe peaches, more time for peaches that might be a little less ripe). Remove with a slotted spoon and dunk into ice water. The peel will come right off!)