Special equipment: a 9-inch springform pan or 8 individual springform pans
For the blackberry-raspberry ice cream: Place the cream, milk, sugar and salt in a saucepan and bring to a low simmer.
Whisk the eggs in a bowl. When cream mixture reaches 130 degrees F on a thermometer, quickly whisk in the eggs. Cook, stirring constantly, until the thermometer registers 170 degrees F. Remove from the heat and pour the custard through a fine-mesh sieve.
Whisk the blackberry puree into the custard, then cool over an ice bath. Transfer to an ice cream maker and freeze according to manufacturer's instructions.
Meanwhile, combine the raspberry puree and sugar in a small saucepan. Bring to a boil and cook until reduced by one-third. Let cool.
When the ice cream is done churning, transfer it to a rectangular container. Drop spoonfuls of the raspberry mixture on top of the ice cream and swirl in with a butter knife. Freeze.
For the lemon-rosemary olive oil cake: Preheat the oven to 350 degrees F. Spray a 9-inch springform pan (or 8 individual springform pans) with vegetable spray.
Combine the sugar and eggs in a stand mixer with the whisk attachment; mix just to combine. With the mixer on low speed, slowly drizzle in the olive oil, making sure the oil is well incorporated and emulsified.
Meanwhile, whisk together the flour, salt, baking powder and baking soda in a bowl.
In a second bowl or a measuring cup, combine the milk, lemon juice, lemon zest and rosemary.
Add the flour to the stand mixer in three additions, alternating with the milk mixture (2 additions). Begin and end with the flour, and be sure to whisk well after each addition--the batter will be runny. Pour the batter in the prepared springform pan.
Bake until the cake is a deep golden brown and bounces back when lightly pressed, 45 to 55 minutes (20 to 25 minutes for individual pans).
Cool to room temperature on a rack, then remove the cake from the pan.
For the lemon-rosemary glaze: In a bowl, whisk together the confectioners' sugar, lemon juice, lemon zest and rosemary until a glaze consistency similar to heavy cream is achieved. Adjust the consistency with more lemon juice or powdered sugar as needed.
For the candied lemon peel: Combine the sugar and 1 cup water in a small saucepan over medium-high heat. Bring to a boil, then turn off heat.
Using a vegetable peeler, peel the zest from the lemons; slice thinly.
Blanch the lemon zest twice in boiling water, changing the water in between. After the second blanching, strain and add the lemon zest to the simple syrup.
Bring the simple syrup to a boil, then turn off the heat and let the lemon zest sit in the simple syrup until translucent and cooled.
For the black salt sugar cookies: In a stand mixer fitted with the paddle attachment, cream together the butter and confectioners' sugar until light and fluffy. Add the vanilla and egg and mix until combined. Add the salt and flour and mix until a dough forms.
Form the dough into a disk, wrap in plastic and refrigerate for 30 to 45 minutes.
Roll out the dough to a 1/4-inch thickness, then cut out cookies using a raindrop-shaped cutter.
Transfer the cookies to a parchment-lined baking sheet and sprinkle lightly with black sea salt and blue sanding sugar.
Bake in a 350-degree oven until golden brown at the edges, 12 to 14 minutes.
For the raspberry coulis: Combine the raspberry puree and sugar in a small saucepan. Bring to a boil and cook until reduced by one-quarter. Let cool.
For the passion fruit coulis: Combine the passion fruit puree and sugar in a small saucepan. Bring to a boil; cook until reduced by one-quarter. Let cool.
To finish: Glaze the cake with the lemon-rosemary glaze and top with the candied lemon peel.
Serve with the two coulis and the ice cream and cookies on the side.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.