Thomas J. Story
To make the aïoli: In a large bowl, whisk together egg yolk, garlic, half the lemon juice, and Dijon mustard. Drizzle in 1⁄2 cup olive oil very gradually, teaspoon by teaspoon, whisking the whole time. Only add more oil when the mixture is opaque. Repeat until all the olive oil is incorporated. Add salt and 1 tsp. cold water and whisk thoroughly. Then slowly whisk in the sunflower oil in the same manner. Once the oil is incorporated, whisk in the remaining lemon juice, and taste for seasoning, adding salt as needed.
To grill the radicchio: Heat a grill to high for direct heat cooking. Drizzle radicchio with olive oil and place it, cut side down, on the grill and cook until charred but not burnt, about 3 minutes. Turn over and cook until charred on that side, another 3 minutes or so.
To serve: Place a generous amount of aïoli on the plate and use the back of
a spoon to spread across the dish. Place charred radicchio over it in the center, and drizzle with muscatel vinegar and extra-virgin olive oil. Garnish with purslane clusters, and sprinkle with flaky salt. Enjoy!