For the genoise: Preheat the oven to 335 degrees F (or 325 if using convection). Grease a half sheet pan and line it with parchment.
In a stand mixer fitted with the whisk attachment, whip the eggs for 5 minutes until light and frothy. With the mixer on medium speed, slowly add the sugar; increase to medium-high speed and beat to a ribbon consistency, another 5 minutes.
Combine the butter and milk in a microwave-safe bowl. Microwave for about 2 minutes, until the butter is melted and the milk is hot. Set aside.
Sift together the flour, baking powder and salt. Set aside.
With the mixer on low speed, add the vanilla and then slowly add the flour mixture; mix until combined, scraping down the sides.
Whisk about 1 cup from the mixer in the hot milk-butter until smooth, then return to the mixer, whisking until just combined.
Pour the batter into the prepared half sheet pan and bake until an inserted toothpick comes out with just a few moist crumbs, 15 to 20 minutes.
Let cool for 15 minutes, then remove the cake from the pan and use a 3-inch biscuit cutter to cut out 12 mini cake rounds.
For the whipped cream: Bloom the gelatin in 2 tablespoons cold water to dissolve.
In a stand mixer with the whisk attachment, beat the mascarpone until smooth and fluffy. Add the confectioners' sugar, beating until smooth. Slowly add the cream; beat until smooth, then add the vanilla. Raise the mixer speed to high and beat to soft/medium peaks.
Mix a dollop of the whipped cream into the gelatin, then add back to the mixer. Whip to medium peaks. Chill until ready to use.
For the caramelized peaches: Toss the peaches, sugar and salt together in a bowl.
Heat a medium-large skillet over medium heat until hot; add the butter. Place the peaches, cut side down, in the skillet and cook, turning once, until caramelized on both sides, 4 to 5 minutes per side; be careful to keep the peach skins intact. Transfer to a parchment-lined baking sheet to cool for about 10 minutes.
To assemble: Place a cake round on a plate and top with two peach wedges, skin-sides facing out.
Scoop some whipped cream into a pastry bag fitted with a large round or star tip and pipe a swirl in the center of the round, between the peach wedges.
Top with a second cake round and pipe another swirl of whipped cream in the center. Garnish with a peach wedge and a wedge of white chocolate if using.
Repeat to make 6 shortcakes total.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.