Preheat the oven to 425 (F). Prepare your 2 pears by removing the stems and core, and dividing each pear into quarters. Slice the quarters into halves, and set aside.
Melt 2 tablespoons unsalted butter in a 10-inch cast iron skillet over medium heat. Add prepared pears (from the 1st step) and sprinkle 1 tablespoon dark brown sugar and 1/4 teaspoon ground cinnamon. Cook, tossing often, until pears are coated and softened. Transfer to a plate.
Allow the skillet to cool slightly and use a damp cloth to wipe out any extra leftover sauce. Once the skillet is clean, transfer to the oven and allow to heat up for 10 minutes, until the skillet is very hot.
While the skillet is heating in the oven, make the batter. In a medium bowl, gently whisk together 3 eggs until the eggs are a pale, uniform yellow, before whisking in 3/4 cup milk, 3/4 cup all-purpose flour, 1 tablespoon natural cocoa powder, 1 teaspoon pure vanilla extract, 1/4 teaspoon salt and remaining 1/4 teaspoon ground cinnamon. Continue whisking until the mixture is a uniform pale brown, and set aside.
Once the skillet is ready and well heated, carefully add the remaining 2 tablespoons of unsalted butter to the skillet, using the handle to rotate the pan and cover its bottom and sides with melted butter. The butter will bubble and splatter, so be careful! Add sauteed pears to the center of the skillet, and pour the rest of the chocolate batter over the pears.
Transfer the skillet to the preheated oven and bake until the pancake is puffed and golden brown around the edges, around 14 to 16 minutes. The center should be set but still custardy. Remove from oven and top with cinnamon; serve immediately, while the pancake is still warm and puffed.