How to Make It
Prepare the cookie: Preheat oven to 325°F. Heat butter in a 9-inch cast-iron skillet over medium until butter melts and foam subsides, 3 to 4 minutes. Pour melted butter in a large bowl, but don’t wipe out skillet. Add oil to butter. Add sugars, vanilla, and cinnamon; whisk vigorously until smooth. Whisk in egg.
Stir together flour and baking soda in a small bowl. Add to sugar mixture, and stir until just incorporated. Fold in oats and raisins. Lightly coat buttered cast-iron skillet with cooking spray. Spread dough in skillet.
Bake at 325°F until just done, 25 to 30 minutes. (The cookie will just be cracking at the edges.) Remove skillet from oven, and cool on a wire rack 15 to 20 minutes.
Prepare the sauce: Heat sugar and butter in a skillet over medium-high, whisking until sugar dissolves. Whisk in miso until smooth. Remove from heat. Add cream; stir in vinegar. Pour half of sauce over cookie. Cut into wedges. Top each serving with 1 tablespoon frozen yogurt, and drizzle evenly with remaining sauce.