Drain the peaches, reserving 2 Tablespoons of the juice. Slice the peaches lengthwise to make them thinner. In a small bowl, combine 1 Tablespoon of melted butter, brown sugar, cinnamon, nutmeg and 2 Tbsp. of the reserved peach juice. Pour in the bottom of a round 9-inch baking pan. Layer peaches on top and then add pecans in the space between the peach slices.
Put milk and vinegar in a bowl and let set for about 5 minutes. You are making a homemade buttermilk. If you don’t have vinegar, you can substitute lemon juice.
In a mixing bowl, cream butter and sugar. Add egg, rum and milk mixture. Add dry ingredients and mix until smooth. Pour batter over peaches in the baking pan.
Bake at 350 degrees for 30 minutes. Let cool for 10 minutes. Inert onto a serving dish. Drizzle 2 tablespoons of rum over the top of the cake.
Let set until cool or overnight but it's best to wait two days for the flavors to meld. Serve cold with whipped cream or warm with vanilla or pecan ice cream. This cake is heavy, so serve small slices.