This quick bread is similar to carrot cake, except it uses parsnips for a unique, more fragrant result. Paired with star anise-spiked apple compote, this is perfect for anything from a holiday brunch to a casual dessert.
Preheat oven to 350 degrees F. Grate the parsnips over the largest hole of a box grater to yield about 2 cups, packed. Set aside. In another bowl, add the dry ingredients: cinnamon, ginger, nutmeg, baking powder, baking soda, salt, and flour. Whisk to combine. Set aside.
In another bowl, add the wet ingredients: brown sugar (technically a dry ingredient, but will mix better with the wet ingredients), vanilla extract, eggs, and vegetable oil. Whisk to combine. Add the dry ingredients to the wet ingredients in batches, whisking after each addition. Fold in the parsnips; batter will look dry at first, but will loosen up as the parsnips release their water. Set aside.
Grease the loaf pan with butter, then spread batter into the prepared pan. Place into the oven on the middle rack. Bake until cooked through, about 40 minutes. Meanwhile, make the Apple Compote.
Apple Compote: In a saucepan over medium heat, add butter, apples, brown sugar, and star anise. Bring to a simmer, uncovered, about 5 minutes. Then cover and continue to simmer at a low heat until apples are soft, 8–10 minutes.
Check cake for doneness: The cake should be golden brown and bounce back to the touch; a knife inserted into the center should come out clean. Place pan on a wire rack and let cool for 5 minutes. Turn the cake out of the pan and continue cooling on the rack, 30 more minutes. Meanwhile, remove Apple Compote from heat and stir in a sprinkle of salt; remove and discard the star anise. Transfer compote to a serving dish.
Assembly: Slice the cake into 1-inch slices, and arrange on a platter. Sprinkle with powdered sugar and serve with Apple Compote on the side.