Step 1Heat the oven to 350 degrees. Generously grease the interior of two (9-inch) round cake pans, both bottom and sides, with butter. If possible, line the bottom of each pan with a 9-inch round of parchment or wax paper and grease it also.
Step 2Sprinkle about 2 teaspoons flour into each pan and shake around until the interior is thoroughly dusted. Turn the pans upside down over the sink and tap against the sink to dislodge any excess flour.
Step 3In a medium mixing bowl, stir 3 cups flour with the baking powder and salt and set aside. In a measuring cup or small bowl, combine the milk with the vanilla and set aside.
Step 4In the bowl of a stand mixer, or in a large bowl using an electric mixer, beat the 1 cup butter until fluffy, 1 to 2 minutes.
Step 5Reduce the speed and add the sugar with the mixer running, continuing to mix until light and fluffy, 2 to 3 minutes more. Add the eggs one at a time and beat into the mixture.
Step 6Add one-third of the milk mixture and beat until absorbed. Add one-third of the flour mixture and beat just until the flour is incorporated. Repeat with the remaining milk and flour in two batches.
Step 7Divide the batter between the two cake pans and smooth the tops with a spatula. Bake the cakes in the center of the oven until the tops are golden brown and the cake starts to pull away from the sides of pan, 25 to 35 minutes.
Step 8Remove the cake pans from the oven and set on a cooling rack or folded towel for 10 minutes. Overturn the cake pans onto a rack or plate, remove the pans and paper from them and return the layers, right side up, to the rack or towel. Wait to frost the cakes until they have cooled to room temperature.
Step 1If the peaches are very ripe and soft, they will not need to be poached; proceed to Step 3. Otherwise, in a 4-quart pot, combine the water and sugar and bring to a boil. Reduce the heat to a simmer, add the peaches and cover them with a small plate or pot lid to keep them submerged.
Step 2Poach until the flesh is easily pierced with a fork or knife, 10 to 30 minutes depending on ripeness. Remove from the heat, drain and cool to room temperature.
Step 3Peel and pit the peaches and cut each into 8 slices. In a medium bowl, combine the peach slices with the lemon juice and cinnamon to coat. Set aside.
Step 1Pour the cream into a mixing bowl and beat at high speed until the cream will hold a soft peak when the mixer blade is lifted from it, about 2 minutes. Add the sugar, vanilla and any liquid from the peach filling and beat until it will hold a firm peak, 2 to 4 minutes more.
Step 2Assemble the cake: Put one cake layer, top side down, on a serving plate or stand. Cover the top with half of the peach filling. Cover the peaches with about 1 cup whipped cream. Set the second cake layer, top-side up, over the first. Arrange the filling on top and frost the sides and the top with the remaining whipped cream. Serve immediately.