Make cake batter: Whisk together dry ingredients in a medium bowl. Then whisk in remaining ingredients until blended.
Prepare a fire for top and bottom dutch-oven cooking (see "How to Use a Dutch Oven", below), but using only 40 briquets. Line a 4-qt. cast-iron camp dutch oven with foil so it comes up the sides to the top.
Make topping: Melt butter in dutch oven, rotating to coat sides. Sprinkle sugar on bottom of pan, then scatter pineapple on top. Gently spread batter over pineapple, cover, and arrange coals on top of pot.
Cook cake, rotating pan every 5 minutes and pushing top coals together as they burn down, until a toothpick inserted in several places comes out with no white dough sticking to it, about 35 minutes. Let cool 10 minutes. Lift cake from pan using foil. Invert onto a plate and gently peel off foil, replacing any pineapple that sticks to it.
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How to Use a Dutch Oven
Prepare the fire. If you have a campfire going, move any large pieces of still-burning wood to the side and level out your hot coals to fit the size of the dutch oven. If the campground doesn't allow wood fires, burn 50 charcoal briquets till they're mostly gray, 10 to 15 minutes, and spread into an even layer the size of the dutch oven.
Set up the oven. For many recipes, you just set the dutch oven on top of the hot coals ("bottom heat cooking"). But there are times when you'll need to heat both the top and bottom of the oven. Just scrape about half the coals to the side and arrange the rest in a circle the size of the dutch oven's outer edge. Set the oven on top of the circle of coals, then pile the rest of the coals on top of the lid.
Start cooking. Lift the dutch-oven lid occasionally to check the food and temperature. To decrease the heat, scrape away some fuel. To increase the heat, or to cook longer than 45 minutes, add 6 to 10 new briquets or more wood embers (from that still-burning wood you moved to the side of your firepit) every 30 minutes.
Note: Nutritional analysis is per serving.