Prepare your pan and oven. Preheat your oven to 350°F (175°C). Line a 9×9 inch baking pan with parchment paper, leaving overhang on two sides for easy removal later.
Make the cranberry filling. In a medium saucepan, combine cranberries, sugar, orange juice, orange zest, and cornstarch. Cook over medium heat for 5-7 minutes until cranberries begin to burst and mixture thickens. Remove from heat, stir in vanilla extract, and set aside to cool slightly.
Prepare the crumble mixture. In a large bowl, whisk together flour, oats, both sugars, baking powder, salt, cinnamon, and nutmeg until well combined.
Cut in the butter. Add the cold butter cubes to the dry ingredients and use a pastry cutter, two forks, or your fingertips to work the butter into the mixture until it resembles coarse crumbs with pea-sized pieces of butter throughout.
Add the egg. Stir in the beaten egg just until the mixture starts to come together. It will still be crumbly, but should hold together when pressed.
Create the base layer. Press about two-thirds of the crumble mixture firmly into the bottom of your prepared pan to form an even crust.
Add the cranberry filling. Spread the cranberry mixture evenly over the crust, leaving a small border around the edges.
Top with remaining crumble. Sprinkle the remaining crumble mixture over the cranberry layer, gently pressing it down slightly.
Bake until golden. Bake in the preheated oven for 40-45 minutes, or until the top is golden brown and the filling is bubbling around the edges.
Cool completely before cutting. Allow the bars to cool in the pan for at least 1 hour, then use the parchment overhang to lift them out. Cut into 16 squares for serving.