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Place an empty, well-seasoned 10" cast iron skillet or other oven-safe skillet of similar size onto the middle rack of the oven. Preheat the oven to 375°F. While the oven and pan preheat, prepare the batter.
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To make the batter: In a medium bowl, whisk to combine the flour, sugar, baking powder, salt, and yeast.
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In a small bowl or measuring cup, whisk to combine the buttermilk, egg, and vanilla.
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Add the wet ingredients to the dry ingredients and whisk briefly to combine. Avoid overmixing; some lumps are OK.
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Add the melted butter and whisk until just combined. Let the batter rest, uncovered, at room temperature for 5 to 10 minutes while you make the filling.
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To make the cinnamon swirl filling: In a small bowl, whisk to combine the brown sugar, cinnamon, and flour, breaking up any clumps. Add 3 tablespoons (43g) of the prepared batter and use a flexible spatula to combine, forming a thick, granular paste.
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Transfer the filling mixture to a piping bag fitted with a plain (round) tip about 1/2" in diameter, or use scissors to cut a 1/2" hole in the end of the piping bag. (No piping bag? Transfer the filling mixture to a zip-top bag and cut one of the bottom corners off to make a 1/2" hole.)
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To assemble the skillet pancake: Once the oven is preheated and the batter has rested, carefully remove the skillet and place it on a rack. Place the butter for the pan in the skillet, allowing it to sizzle, melt, and coat the bottom. Pour the pancake batter into the pan, spreading it as needed to cover the bottom completely.
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Pipe the cinnamon swirl filling in a spiral pattern on top of the batter. It will sink slightly into the batter; that's OK.
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Carefully return the skillet to the oven and bake for 20 to 25 minutes, until the top is set and the edges of the pancake are golden brown and pulling away from the sides.
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To serve, top the Cinnamon Roll Skillet Pancake with a pat of butter and maple syrup. Serve immediately, directly from the skillet. (Slice using a dull blade, like a nylon spreader or butter knife, to prevent damaging the skillet.)
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Storage information: Store leftover Cinnamon Roll Skillet Pancake in an airtight container in the refrigerator for up to 2 days. Reheat on a wire rack placed on top of a baking sheet in a 200°F oven for 10 minutes or until warm.