For the vanilla brown butter cake: Preheat the oven to 350 degrees F. Line the bottom of a 13-by-18-inch baking sheet with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, combine the powdered sugar, almond flour, all-purpose flour and egg whites and mix on low until the ingredients combine without any visible lumps, approximately 1 minute.
Meanwhile, put the butter and scraped vanilla bean seeds in a 2-quart saucepan and cook on high heat, whisking occasionally. As the mixture cooks, the butter will begin to brown and it will start to smell amazing, about 15 minutes! The longer the butter and vanilla stay on the heat, the more "nutty" the final flavor will become. So cook it to your preference. Strain the mixture through a fine-mesh strainer into a bowl, reserving the brown butter.
Turn the stand mixer to the lowest speed and stream the hot brown butter into the batter, mixing for approximately 2 minutes.
Transfer the cake batter to the prepared baking sheet and bake until a cake tester comes out clean, 8 to 10 minutes. Let cool, then cut into rectangles about 4 inches by 1 1/2 inches.
For the toasted marshmallow sauce: In a small saucepan, combine the granulated sugar and 1/4 cup water and mix until the sugar is dissolved. Add the corn syrup to the sugar/water mixture. If there are any granules of sugar on the side of the saucepan, brush them down using a pastry brush dipped in water.
Add the egg whites to the bowl of a stand mixer fitted with a whisk attachment. Mix the egg whites on high speed until soft peaks appear, then turn the mixer down to medium speed.
Place the saucepan on medium-high heat and cook the sugar mixture to thread stage, approximately 234 degrees F. Turn the stand mixer to high speed and stream in the cooked sugar. Continue to mix the meringue on high speed until the outside of the bowl feels cool to the touch, approximately 5 minutes.
For the spring fruit and berry compote: Combine the blueberries, raspberries, strawberries, figs, granulated sugar and mint in a mixing bowl and toss together. Let stand at least 5 minutes
For the mint oil: Put the oil and mint in a blender and blend for 1 to 1 1/2 minutes. Transfer to a saucepan, slowly bring to a simmer and cook for 1 to 2 minutes. Strain with a fine-mesh strainer, then let cool. Transfer the cooled mixture to a squeeze bottle.
To assemble: Spoon and drag about 2 tablespoons of the marshmallow onto each plate and toast the top with a kitchen blowtorch. Place a rectangle of cake on top of each, then divide the fruit among the cakes. Decorate the plates with the mint oil from the squeeze bottle.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.
Propane gas torches are highly flammable and should be kept away from heat, open flame and prolonged exposure to sunlight. They should be used only in well-ventilated areas. Follow torch manufacturer's instructions for use.