Prepare a fire (see "How to Bake in a Dutch Oven," below).
Meanwhile, in a large bowl, whisk eggs and flour until smooth. Then whisk in milk, salt, and sugar until blended.
Set a 6-qt. dutch oven over a ring of coals as directed and add butter. When butter melts, stir to coat pan and pour in batter. Scatter 1 1/2 cups berries on top. Cover with lid and more coals as directed below. Cook until Dutch baby is puffed and deep golden all over with no liquid in the center, 20 to 25 minutes.
Scatter remaining 1/2 cup berries over Dutch baby. Cut into wedges and serve with syrup.
How to Bake in a Dutch Oven
Lewis and Clark brought one to the wilderness. So did the early pioneers to Utah (it's now the official state cooking vessel). And so should you, because it means you'll get to bake--and eat--carbs in camp. All you need is a 6-qt. camp dutch oven (one with legs and a flanged lid; lodgemfg.com), some regular (not competition-style) charcoal and a chimney or hot embers from a wood campfire, and a heatproof spot like a fire ring or bricks set flat on an area free of flammable material; check your campground's fire rules.
Prepare the fire. If using charcoal: Light 50 briquets in a chimney and burn till they're spotted gray, 15 minutes. If using a campfire: Scrape the fire to the side, level out a space the size of the dutch oven, and mound the hot embers nearby (2 to 3 qts. worth).
Lay a bottom ring of hot coals. The area of the coals should be slightly smaller than the circumference of the dutch oven. Put the oven on top and set the lid in place.
Lay a top ring of hot coals. Use metal tongs to arrange a single ring on top of the lid around the lip. Evenly space a few more coals across the lid. Set any extra heated fuel aside. To check the food and temperature, lift the lid occasionally.
Tweak the temperature. To decrease heat, scrape away some fuel. To increase heat, or to cook longer than 45 minutes, add 5 or 6 new coals to both the top and the bottom of the dutch oven (touching lit ones so they'll ignite) about every 30 minutes.