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1
Preheat the oven to 325F.
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2
Halve or cut the fruits, and reserve the juices. (Something like 1/2-inch pieces will do just fine.)
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3
Beat the egg yolks with the sugar, milk and fruit juices until creamy. Add the vanilla extract and flour, and mix until fully combined.
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4
Beat the egg whites until stiff. Gently fold the whites into the cake batter.
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5
Grease and flour a 9x13-inch baking pan. Pour the batter into the pan and spread it with spatula. Arrange the fruit on top of the batter. (It will be a lot of fruit, but go for it.)
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6
Bake for about 25 minutes, until a toothpick inserted in the center of the cake comes out with a few moist crumbs attached. (It's very important not to over-bake, so watch carefully. It will be done when it is barely done -- the crust will bubble up and cover the fruit partially, but the center should be very moist and close to creamy.)
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7
Remove the pan from the oven, let it cool completely and place in the fridge for about three hours or overnight.
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8
About half an hour before serving, mix the cream with the basil leaves (use whole leaves, do not chop).
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9
Serve the cobbler chilled, with a couple of drops of basil cream on top.