Grease a 10-inch cast iron skillet or heavy-bottomed skillet with butter or oil. Set aside.
In a medium bowl, whisk together the flour, sugar, baking powder, and salt.
In a separate bowl, whisk the melted butter (or oil), milk, egg, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients. Stir until just combined—do not overmix. A few lumps are fine.
Spread the blackberries evenly over the bottom of the prepared skillet. Pour the batter gently over the berries, spreading it to the edges.
Place the skillet on a camp stove. Set up a heat diffuser: fold a sheet of heavy-duty aluminum foil into a 12x12-inch square, then crumple it slightly and place it under the skillet. This prevents direct heat from scorching the bottom.
Light the stove and set to low heat. Cover the skillet with a tight-fitting lid or a large sheet of foil crimped around the edges.
Cook for 30 to 40 minutes, rotating the skillet a quarter turn every 10 minutes for even baking. Check doneness with a toothpick after 30 minutes.
Once done, remove from heat. Let the cake rest in the skillet for 5 minutes. Serve warm, directly from the skillet. A dollop of yogurt or a dusting of powdered sugar is nice but optional.