Position an oven rack in the center and preheat the oven to 350 degrees F (175 degrees C). Grease a nonstick 9-inch round cake pan.

Place butter in a saucepan over medium-high heat; stir until melted. Add 1/3 cup white sugar, brown sugar, and cinnamon. Increase heat slightly and stir mixture until it comes to a gentle boil. Cook for 30 seconds, remove from heat, and immediately scrape mixture into the prepared cake pan. (Be careful as mixture will be very hot.) Tilt the cake pan to evenly coat the bottom. Sprinkle cranberries evenly on top of the sugar mixture; set aside.

Whisk together flour, baking powder, and salt in a medium bowl.

Beat butter in a large bowl with an electric mixer on medium speed until fluffy. Gradually beat in remaining 2/3 cup sugar. Add eggs, one at a time, beating well after each addition. Mix in orange zest, orange extract, and vanilla extract. Blend in buttermilk. Gradually add flour mixture, beating briefly until smooth. Fold in chocolate chips. Drop heaping spoonfuls of the batter randomly over cranberries in the cake pan, then smooth the batter with the back of a spoon until even.

Bake in the preheated oven until cake is golden brown, springy to the touch, and a toothpick inserted into the center comes out clean, 40 to 45 minutes. Cool on a wire rack for 15 minutes. Run a table knife around the edges to loosen. Invert carefully onto a large, flat serving plate. Cool for at least 20 minutes before serving.