For caramel-vanilla oranges: Peel and segment oranges into a medium bowl. In a medium saucepan, cook sugar and water over medium heat until sugar dissolves and liquid is clear, about 2 minutes.
Increase heat to medium-high and continue to cook until sugar is a pale gold caramel color, about 2 minutes. Do not stir once sugar begins to boil; it may cause sugar to crystallize. Once it starts to color, you can gently swirl the pan so that it colors evenly.
When caramel is a medium tan color, remove from heat and slowly and carefully add 1 tbsp. of the orange juice. The hot liquid will bubble up and sputter. Once it has stopped sputtering, add a couple more tablespoons of orange juice and again wait until caramel stops sputtering. With a wooden spoon, gently stir in the rest of the orange juice and vanilla.
Pour orange caramel over orange sections. Let marinate for at least 10 minutes before serving, or cover the bowl with plastic wrap and leave at room temperature overnight.
For torte: Preheat oven to 350 degrees. Grease the bottom and side of a cake pan with nonstick cooking spray or butter and coat evenly with flour, knocking out the excess.
Spread walnuts in one layer in a small baking pan and put in the (preheated) oven. Set a timer for 10 minutes and check walnuts to see if they're a light golden brown. If not, toast 2 minutes longer.
In a food processor, process walnuts with 1/4 cup of the flour until they're finely ground and look like coarse sand, with a few larger visible pieces of walnut. By hand, stir in the remaining 1/2 cup flour and baking powder and set aside.
In a stand mixer with a paddle or handheld mixer and medium bowl, beat butter and sugar on medium speed until smooth. Add egg, rum and orange zest and mix until well combined, using a rubber spatula to scrape down the side of the bowl. Add flour-walnut mixture; reduce speed to low and mix until batter is smooth and well combined.
With the spatula, scrape batter into prepared cake pan and spread evenly. Bake until a bamboo skewer or toothpick inserted in the center comes out clean and cake springs back in the center if you press it with your finger, 20 to 25 minutes.
Cool cake to room temperature. Cut around the inside edge with a knife, then remove cake by inverting it onto a platter or plate.
To serve: Cut torte into 8 wedges. Put a spoonful of caramel oranges alongside each piece.
The Fearless Baker (Little, Brown, and Co. 2011)