For brownie batter: In the top of a double boiler, combine chocolate and butter. Cook over simmering water, stirring occasionally, until smooth. Turn off heat, and whisk in sugar. Remove from heat, and let cool slightly. Whisk in eggs and vanilla.
In a medium bowl, whisk together flour, cocoa, and salt. Fold flour mixture into chocolate mixture just until combined. Set aside.
For snickerdoodle dough: In the bowl of a stand mixer fitted with the paddle attachment, beat butter and sugar at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add egg, beating well. Beat in vanilla.
In a medium bowl, whisk together flour, salt, cinnamon, and baking powder. Gradually add flour mixture to butter mixture, beating just until combined.
Spray a 9-inch round cake pan with baking spray with flour. Spoon large dollops (about 3 tablespoons each) of brownie batter into bottom of prepared pan, leaving space between each. Crumble and sprinkle snickerdoodle dough in between brownie batter. Top with any remaining brownie batter and snickerdoodle dough. Tap pan on counter to level top.
Bake until a wooden pick inserted in center comes out with a few crumbs, 30 to 35 minutes.
Meanwhile, for cinnamon sugar: In a small bowl, stir together sugar and cinnamon.
Remove brookie from oven, and immediately sprinkle with cinnamon sugar. Serve warm in pan, or let cool completely, and remove from pan.
Recipe by Bake from Scratch at https://staging.bakefromscratch.com/snickerdoodle-brookie/