Preheat oven to 400 degrees. Put 2 tablespoons butter in a 9" x 13" pan and place in the oven while it's preheating.
Add the flour, eggs, milk, and salt to a blender and process until smooth.
When the oven is preheated, carefully take out the hot pan and swirl around the now melted butter to coat the pan. Pour the blender mixture into the pan and bake for about 20 minutes. It will be done when it's puffed up and light golden brown.
While the pancake is cooking, start the sauce. Add the sugar, buttermilk, and corn syrup to a medium saucepan with the remaining 1/4 cup butter. Heat over medium heat, stirring frequently until boiling, then reduce heat to medium low and cook uncovered for about 6 minutes, continuing to stir frequently.
Add the baking soda. It will bubble and increase in size, then gradually turn a light golden brown. Remove from heat, add the vanilla, stir, and patiently wait for the pancake to finish in the oven.
Serve the pancake with the buttermilk syrup.