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Preheat the oven to 350°F with a rack in the center. Line the bottom of an 8" round pan with a parchment round and lightly grease the bottom. Leave the sides of the pan ungreased.
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To make the peach topping: Bring a pot of water to a boil and score the bottoms of your peaches with an “X” shape about 1/2" big. Boil the peaches for 30 seconds, then transfer them to an ice bath. Remove the skin using a paring knife or your fingers; they should come off easily. (See this process demonstrated in our blog post, How to peel a peach without a knife.) Slice the peaches in half, remove the pits, then cut each half into thirds. You should have about 2 cups peach slices (300g). Set aside.
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In a wide, heavy-bottomed pot or pan, distribute the sugar and salt in an even layer. Cook over medium heat, watching carefully but not stirring, until large swaths begin to melt, 4 to 5 minutes. (You can tilt or rotate the pan occasionally to encourage even melting.) Once there are large patches of liquified sugar, stir gently with a flexible spatula until all of the sugar has melted and begins to brown. Turn down the heat if the sugar is browning too quickly. Once the sugar has reached a deep amber color, about 2 minutes, immediately transfer the caramel to the prepared pan and tilt the pan to spread it to the edges. Set aside to cool slightly; the caramel will harden. Lay the peach slices over the cooled caramel to completely cover the bottom of the pan. (Devour any slices that don’t fit!)
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To make the sponge cake: In the bowl of a stand mixer fitted with the whisk attachment, combine the eggs, sugar, and salt. Starting on low speed and gradually increasing to the highest setting, whip the mixture until pale, foamy, and tripled in volume, 8 to 10 minutes. When you raise the whisk and let some batter fall onto the surface, it should “ribbon” into the bowl (i.e. sit on the surface of the batter for a couple seconds before losing its shape).
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Remove the bowl from the mixer and whisk in the vanilla. Sift the flour evenly over the eggs, then use a whisk to gently fold the flour into the egg mixture, taking care not to deflate it. Use a spatula to scrape along the bottom and sides of the bowl to incorporate any hidden pockets of flour, then gently transfer the batter to the pan with the peaches. Don’t worry about evening out the surface — it’ll level out as it bakes.
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Bake the peach upside-down cake for 35 to 40 minutes, or until the surface is deep golden brown and springs back when lightly pressed, and a toothpick or paring knife inserted into the center comes out clean.
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Transfer the cake to a wire rack and let it cool for 10 minutes. Run a small offset spatula or dull knife around the circumference of the pan to loosen the edges, then invert it onto a serving plate or wire rack. Let it cool for an additional 20 minutes before serving. While the cake cools, whip the cream.
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To make the whipped cream: Using a stand mixer fitted with the whisk attachment, a large bowl and a hand whisk, or a Mason jar, whip together the heavy cream, salt, and confectioners’ sugar until it holds soft peaks. Serve the whipped cream with slices of the peach upside-down cake or cover and store in the refrigerator until ready to serve, up to 2 hours ahead.
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Storage information: Leftover peach upside-down cake can be stored airtight in the refrigerator for up to 1 week. Remove and warm in a 350°F oven for 10 minutes before serving.
