Preheat oven to 350F. (regular bake setting/not fan assisted) and grease a 10-inch top diameter cast iron skillet (or 9-inch cake pan).
Make the cinnamon streusel: Stir together the flour, brown sugar and cinnamon. Add the cold butter and use your fingertips to rub the butter into the dry mixture until it is crumbly. Set aside.
In a small saucepan, add the 6 Tbsp of butter. Cook over medium heat until butter is foamy and golden-brown, about 5 minutes. Immediately pour into a small bowl (to stop the cooking). Add the pinch of cinnamon and stir. Allow browned butter to cool until just lukewarm.
In a medium bowl, whisk together the flour, baking powder and salt. Set aside.
Prepare the pears: Cut pears in half lengthwise. Using a small spoon, scoop out the core and scrape a bit of the tough spine that runs up to the stem away. Place pear halves on a cutting board, cut side down. Using a sharp knife, make 5 or 6 thin, even slices in the pear halves, starting from about 3/4-inch down from the top, stem-end of the pear. Set aside.
In a large bowl with an electric whisk (or hand whisk) or the bowl of a stand mixer fitted with the whisk attachment, add the cooled brown butter, the vegetable oil and the white sugar. Whisk together until light and well combined, about 1 minute. Add the egg and vanilla and whisk 1 minute more. Add the sour cream and whisk until well combined. Remove bowl from stand mixer, if using.
Using a spatula, add 1/3 of the flour mixture to the wet mixture and gently fold in until combined. Add half of the remaining flour mixture and gently fold in until combined. Add the remaining flour and fold in until no flour is visible. Batter will be quite thick.
Spoon batter into prepared cast iron skillet or baking pan and level. Sprinkle cinnamon streusel evenly overtop of the batter. Fan the sliced pear halves and place on top of the cake randomly, pressing into the batter just slightly. (You may only be able to fit 5 of the 6 pear halves, depending on the size of your pears).
Bake in preheated oven for 45-60 minutes, or until puffed and golden on top and the cake part tests clean with a cake tester. Serve warm from the pan or at room temperature. Serve with whipped cream or ice cream, if desired.
Notes
Unsalted butter makes the best browned butter and is less likely to burn. You can use salted butter if that's all you have. Just watch extra carefully to avoid burning.Be sure to read the notes above this Recipe Card, where I share more detailedtips, variations and substitution suggestions for this recipe!