For topping: In a medium bowl, whisk together flour, granulated sugar, cinnamon, and salt. Using a fork, stir in melted butter and vanilla until well combined and mixture is crumbly. Refrigerate until ready to use.
Preheat oven to 350°F (180°C). Spray an 8-inch square baking pan with baking spray with flour. Line pan with parchment paper, letting excess extend over all sides of pan.
For cake: In the bowl of a stand mixer fitted with the paddle attachment, beat butter, granulated sugar, ¼ cup (55 grams) brown sugar, and oil at medium speed until light and fluffy, 3 to 4 minutes, stopping to scrape bottom and sides of bowl. Add eggs, one at a time, beating well after each addition. Beat in vanilla.
In a medium bowl, whisk together flour, baking powder, salt, and baking soda. With mixer on low speed, gradually add flour mixture to butter mixture alternately with sour cream, beginning and ending with flour mixture, beating until just combined after each addition and stopping to scrape bottom and sides of bowl.
In a small bowl, whisk together cinnamon and remaining ¼ cup (55 grams) brown sugar.
Spread half of batter (about 2½ cups or 595 grams) into prepared pan. Sprinkle cinnamon sugar onto batter, leaving a ½-inch border on all sides. Using an offset spatula, carefully spread remaining batter onto cinnamon sugar. Sprinkle topping all over batter.
Bake until edges are golden brown and an instant-read thermometer inserted in center registers 205°F (96°C), 1 hour to 1 hour and 10 minutes. Let cool in pan for 10 minutes. Using excess parchment as handles, remove from pan, and let cool slightly on a wire rack. Best served warm. Garnish with confectioners’ sugar, if desired. Store in an airtight container for up to 3 days.