Preheat the oven to 350°F with a rack in the center position. Grease a 10-inch Bundt pan with cooking spray and evenly sprinkle ½ cup of the walnuts in the bottom.
In a large, plastic zip-top bag, combine the sugar and cinnamon. Shake to mix well.
Cut each biscuit into quarters. Working with about 12 biscuit pieces at a time, add them to the bag with the cinnamon sugar. Seal and shake until well coated. Add a layer of coated biscuit pieces to the prepared pan. Sprinkle with about ¼ of the remaining walnuts. Repeat layering with remaining biscuits and walnuts, ending with biscuits.
Melt the butter in a medium saucepan over medium-low heat. Stir in the brown sugar and vanilla and cook, stirring constantly, until combined and smooth, about 1 minute.
Pour the butter mixture over the biscuits and gently shake the pan to distribute. Bake for 30 to 35 minutes, until deep golden brown and no longer doughy in the center.
Run a spatula around the edges to loosen and let cool for 5 minutes. Place a serving plate upside down on the pan and carefully flip. Let sit for 1 minute, then remove the pan. Serve warm.
