Place butter inside a 9-inch cast iron skillet, casserole dish or pie plate (avoid glass, as it can shatter), then place it in the oven on the center rack and turn it on to 450 degrees F. If using vegan butter or non-stick spray, leave the skillet dry.
While the oven preheats, mix together the eggs, milk, vanilla, maple syrup, oat flour and salt. I like to do this in a blender or with an immersion blender since it's faster, but you can also use a whisk. Make sure there are no lumps remaining.
When the oven is preheated, check to make sure the butter is melted. I like to let it go until it starts to brown and smell nutty, but that step is optional. Remove the skillet from the oven, pour the batter inside, then place it right back in. If using vegan butter or cooking spray, add it to the pan before pouring in the batter.
Lower the oven temperature to 425 degrees, then bake for 15-20 minutes until it's puffed up, no longer jiggly and browned around the edges. Very important - keep the oven closed the entire time it bakes.
Slice into wedges and serve immediately with more butter and maple syrup on the side. Leftovers can be sliced into wedges, placed in a zip-top bag and frozen. Reheat in a toaster oven or microwave.