Grease a 10-inch cast iron skillet generously with butter. Set it aside.
In a medium bowl, whisk together 1.5 cups flour, sugar, baking powder, and salt until combined.
In a small bowl, beat the egg, then whisk in the milk, melted butter, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients. Stir with a spatula just until no dry flour remains. The batter will be thick—do not overmix.
Toss the blueberries with the remaining 1 tablespoon of flour. Gently fold them into the batter with a few strokes.
Scrape the batter into the prepared skillet and spread it evenly. The batter will be quite thick; use the spatula to coax it to the edges.
Place the skillet on a camp stove over low heat. Cover with a lid or a piece of heavy-duty aluminum foil tented slightly to avoid touching the batter.
Cook for 25–30 minutes, rotating the skillet a quarter turn every 8 minutes to prevent hot spots. The cake is done when a skewer inserted in the center comes out clean or with a few moist crumbs.
Remove from heat and let cool in the skillet for 5 minutes. Slice and serve warm.