In a large mixing bowl, combine the all-purpose flour, white granulated sugar, dark brown sugar, baking powder, salt, ground cinnamon, and ground nutmeg. Whisk these dry ingredients together until well combined.
To the dry mixture, add the lightly beaten eggs, milk, and canola oil. Stir gently with a rubber spatula until just combined. Be careful not to overmix; a few lumps are okay!
In a separate bowl, mix the frozen blackberries, frozen blueberries, orange juice, and the grated orange zest. This will be the juicy filling of your cobbler.
Grease your 9-inch round cake pan. Pour the berry mixture into the bottom of the pan, then gently spoon the cobbler batter over the top. Spread it out evenly; it doesn’t have to cover every berry.
Pour 1 cup of water into the bottom of the Instant Pot. Place the trivet inside. Carefully lower your cake pan onto the trivet.
Close the Instant Pot lid and set it to cook on high pressure for 25 minutes. Once the cooking time is complete, allow a natural release for about 10 minutes, then carefully perform a quick release to release any remaining pressure.
Once the pressure is released, carefully remove the pan from the Instant Pot. Allow the cobbler to cool slightly before serving. For the ultimate indulgence, serve warm with a scoop of vanilla ice cream on top.