Preheat oven to 425 degrees F and heat a 10-inch cast-iron skillet over moderate heat. In a medium bowl, whisk the eggs with the grated lemon zest, granulated sugar and salt until combined. Add the flour and milk and whisk until the batter is completely smooth. Gently stir 1 cup each of the fresh raspberries and blackberries into the pancake batter.
Melt the butter in the cast-iron skillet and add the berry pancake batter, gently spreading the fruit in the batter so that it is evenly distributed. Bake the Dutch Baby in the center of the oven for about 22 minutes, until the edge is browned and puffed and the center of the pancake is lightly browned in spots. Transfer the skillet to a trivet and use a fine-mesh sieve to dust the Dutch Baby with confectioners’ sugar. Cut the pancake into wedges and serve immediately, with the remaining fresh raspberries and blackberries.