Set the oven to 350 degrees. Line a rimmed half sheet pan with aluminum foil and grease or butter well. Set aside.
In a bowl, combine the cake flour, soda, powder, and salt. Set aside.
In the bowl of a stand mixer or in a large bowl using an electric hand mixer, cream together 1/2 cup butter and sugar. Add one egg at a time until incorporated. Add the 2 teaspoons vanilla, oil, yogurt, and tea and mix to combine. Slowly add a third of the dry ingredients to the wet and stir to combine. Continue to add the dry ingredients to the wet in thirds until the two are completely combined. Pour into the lined sheet pan and smooth into an even layer. Bake in the middle of the oven until a toothpick inserted into the middle comes out clean – about 18 to 20 minutes.
Remove the cake from the oven and allow to cool in the pan. Gently lift the foil to remove the cake from the pan. Cut the cake into two large, even rectangles and wrap each well in plastic wrap. Freeze the two cakes for at least one hour, or overnight, before assembling.
Make the curd: In a glass bowl set over a pot of boiling water, combine the peach puree, sugar, and yolks and bring to a simmer. Continue to cook until the mixture thickens and easily coats the back of a spoon – about 15 to 20 minutes.
Carefully remove the bowl from the heat and add a tablespoon of butter, stirring until completely melted before adding another. Stir in the lemon juice and let cool on the counter for about 15 minutes. Transfer to an airtight container or Mason jar and store in the fridge until ready to assemble.
Make the buttercream: In the bowl of a stand mixer or in a large bowl using an electric hand mixer, cream together the remaining butter and powdered sugar. Add the remaining vanilla and a pinch of salt and beat again until just incorporated. Transfer to an airtight container and refrigerate until ready to use or straight into a piping bag (if your house is warm and humid, keep the bag in the fridge, too).
Make the fruit leather confetti: Simply cut small circles out of the fruit leather using whatever tools you have around the house. The end of a small straw, the small opening at the end of a round piping tip, expert knife skills and patience etc.
To assemble: Remove cakes from freezer and cut into small rounds using a biscuit or cookie cutter (I used a 3-inch round).
Place a single cake in the center of a plate. Pipe a thick ring of buttercream about an 1/8th of an inch from the edge of the cake, leaving the center empty. Fill the ring with a tablespoon or so of peach curd. Top with another cake and repeat with buttercream and curd. Place a final third layer on top and frost with a full layer of buttercream, smoothing with a wet knife. Sprinkle with fruit leather confetti. Continue with other cakes and frosting until you have a small collection of mini cakes. Serve with iced tea and fresh peach slices.