Preheat oven to 425°F. Line a baking sheet with parchment paper.
In a large bowl, use a fork to whisk together 1 cup flour, 2 tablespoons sugar, 2 teaspoons baking powder, a pinch of kosher salt, and 1/3 cup chocolate chunks. Add 4 tablespoons cubed butter and use your fingers to pinch the butter into the flour until the butter crumbles are the size of small peas. Use the fork to stir in ⅓ cup heavy cream.
Transfer the dough to the parchment-lined baking sheet, wet your hands (so that they won’t stick to the wet dough) and pat the dough into a 1-inch thick, 5x5-inch wide square. Cut into 4 or 6 shortcakes, depending on how many people you’re serving, but do not pull them apart. We want to bake them while touching each other.
Press a few chocolate chunks into the tops of each shortcake, then brush with heavy cream and sprinkle generously with sugar and 1/2 teaspoon flaky sea salt.
Bake for 15 minutes, until golden brown on the bottom edges. They shouldn’t look brown on top. Cut shortcakes apart down the cut lines you already created, spread them apart, and allow to cool for at least 5 minutes.