(Makes 1 quart)
1 1/3 cups sugar, divided
2 tablespoons water
4 tablespoons unsalted butter, divided
1 teaspoon fine sea salt
7 oz bittersweet (60-70% cacao) chocolate, chopped
1 1/2 cups whole milk
3/4 cup heavy cream, divided
1/3 cup unsweetened cocoa powder
5 large egg yolks
8 waffle cups
1/4 cup extra-virgin olive oil
Flakey sea salt for garnish
Combine 1 cup of sugar and water in a small sauce pot on medium-high heat. Cook until golden amber color, about 15 minutes; remove from heat. With a wooden spoon, carefully stir in 2 tablespoons unsalted butter and sea salt; stir in 1/4 cup of heavy cream. Set aside.
Melt together chopped chocolate and 2 tablespoons unsalted butter in a non-reactive bowl over a pot of simmering water on medium heat.
Heat milk, 1/2 cup heavy cream, and cocoa powder in a medium saucepot, whisking occasionally. Bring to a simmer; remove from heat.
Combine yolks and 1/3 cup of sugar in the bowl of a stand mixer with the whisk attachment. Whisk on medium speed until incorporated and light in color.
Still whisking, gradually ladle half of milk mixture into creamed egg mixture to temper eggs. Slowly add melted chocolate into the eggs. Stir custard mixture back into the saucepot. Cook until it starts to thicken so that it coats the back of a spoon and temperature reaches 170˚F.
Strain mixture through a fine mesh strainer into a bowl; set bowl over an ice bath. Refrigerate overnight, or until it reaches 40˚F. Pour cream into an ice cream maker and churn for 15 minutes until partially thickened, pour in caramel while machine is churning, continue for about 15 additional minutes.
Serve chocolate ice cream in a waffle cup with a tablespoon drizzle of extra-virgin olive oil and sprinkle with sea salt.