Preheat the oven to 425°F. Whisk the eggs together. Whisk in half the milk. Add the flour, sugar and salt and whisk until completely smooth. Whisk in remaining milk and vanilla extract. Let the batter rest for minutes. This helps hydrate the flour and gives a more tender texture.
While the batter is hydrating, heat the pan in the oven for about 10 minutes.
Carefully remove the hot baking dish from the oven. Swirl the melted butter around the bottom of the pan and use a silicone brush to brush it on the sides of the pan. Immediately pour in the batter. Bake until deeply golden, puffed throughout and just set, about 27-35 minutes. The pancake will puff dramatically in the oven and settle as it cools. That's exactly what you want.
Cut into squares and serve immediately with desired toppings.
Notes
Preheat your baking pan. This step is essential! A hot pan helps the batter begin setting immediately and encourages browning while helping prevent sticking.
Use a sturdy metal baking pan. Avoid glass baking dishes such as Pyrex for this recipe. Pouring cooler batter into a very hot glass dish can cause thermal shock and potentially shatter the glass.
Keep the oven door closed. Avoid opening the oven during baking, as a sudden drop in temperature can interfere with the pancake's rise.
Expect some deflation. Your Swedish Oven Pancake will puff up as it bakes and settle somewhat after coming out of the oven. This is completely normal!
To store and reheat leftovers: Wrap any leftover pancakes tightly and store them in the refrigerator for up to 3 days. Reheat in a skillet on the stovetop with a little butter or in the microwave or a low oven until warmed through.