Sift the flour, cocoa powder, baking soda, espresso powder, salt and 3/4 cup sugar into a large bowl. Whisk in the chocolate and set aside.
Add the egg whites and cream of tartar to the bowl of a stand mixer fitted with the whisk attachment. Whip the whites on medium-high speed until foamy, about 30 seconds. Slowly pour in the remaining 3/4 cup sugar and whip on high speed until the whites are glossy and can hold a stiff peak. Add the vanilla and beat to combine. Remove the bowl from the mixer.
Gradually add the flour mixture, gently folding it into the egg white mixture, until fully combined. Spoon the batter into an ungreased 10-inch tube pan and bake until the cake springs back when pressed with a finger, 30 to 35 minutes. Do not open the oven during this time. Let cool, inverted, for 1 hour before removing the cake from the pan.
To grill the cake: Preheat an outdoor grill or grill pan over medium-high heat. Slice the cake and brush both sides of each slice lightly with the butter. Grill the cake slices until the surface becomes lightly caramelized and grill marked, about 1 minute per side. Serve with the berries, a dollop of whipped cream and a sprinkling of grated chocolate.