(Nutrition information is calculated using an ingredient database and should be considered an estimate.)
In a stand mixer fitted with the paddle attachment or a large mixing bowl with a hand mixer, mix together milk, sugar, egg, egg yolk, melted plant butter, and yeast.
Add just 3 cups of flour and salt and mix until a dough forms. Switch to the dough hook (or knead by hand on a floured surface) and knead the dough for 3-5 minutes, until the dough pulls away from the sides. The dough should be moist, but if it’s too sticky to handle, add up to ¼ cup more flour, 1 tablespoon at a time.
Cover the mixing bowl and let the dough rise in a warm place until doubled in size, about 1 hour.
Meanwhile prepare the cinnamon filling. Mix the brown sugar and cinnamon together in a small bowl and set aside. Brush 1-2 tablespoon softened plant butter on the bottom and sides of a 9-inch cast-iron skillet or 9-inch cake or pie pan.
When the dough is done proofing, knead the baking powder into the dough with the dough hook or by hand, until smooth.
On a well-floured surface, roll the dough out until a 12x18-inch rectangle, squaring off the corners. Brush the soft plant butter over the entire surface and sprinkle the cinnamon brown sugar evenly over the butter, patting it down to stick.
Cut the dough into 6 long 2x18-inch strips. Tightly roll up one strip and place it in the center of the prepared pan. Matching up the ends, add another strip, rolling it around the first one to create one large cinnamon roll. Repeat with all strips. Cover and let rise for another 30-45 minutes.
Preheat the oven to 375°F. Bake the cinnamon roll for 35-40 minutes, rotating the pan halfway through. If parts of the cinnamon roll get dark toward the end, tend the cinnamon roll loosely with foil to prevent it from getting too browned.
Meanwhile make the icing. Cream the plant butter until light and fluffy. Add the powdered sugar and vanilla and mix until smooth. Add oat milk until thin but spreadable. Spread icing over the warm cinnamon roll. Slice and serve.