Position a rack in the middle of the oven; preheat to 400 degrees. Line a baking sheet with parchment paper. Make the shortcakes: Whisk the flour, granulated sugar, cocoa powder, baking powder and salt in a large bowl. Using your fingers, rub the butter into the flour mixture until sandy. Add the chocolate. Whisk 1 egg, the cream and vanilla in a glass measuring cup; stir into the flour mixture with a fork to make a shaggy dough (there will be some dry bits). Turn out onto a lightly floured surface; pat flat until 1 1/2 inches thick. Cut into 6 rounds with a knife or cookie cutter, using the scraps for the last cake.
Place the rounds on the baking sheet; freeze for 20 minutes. Beat the remaining egg; brush onto the cakes and sprinkle with raw sugar. Bake until firm, about 20 minutes. Transfer to a rack to cool.
Meanwhile, make the toppings: Toss half of the strawberries with half of the sugar in a bowl; set aside. Place the other half of each in a saucepan; cook over medium-low heat, mashing with a fork to make a thick puree, about 10 minutes. Cool completely. Whip the cream with a mixer until medium peaks form; swirl in the strawberry puree.
Split the shortcakes in half. Layer some of the strawberry cream and reserved fruit on the bottoms; cover with the shortcake tops. Finish with more strawberry cream and the remaining berries.