For cake:

1. Preheat oven to 350ºF/180ºC.
2. Butter and flour a large 10 or 12-cup bundt pan. Refrigerate while making the batter.
3. If you can, toast the nuts: scatter the pieces on a baking sheet and bake in a 325°F/160°C oven for about 10 minutes or more as needed. They will have a toasted color and the smell will be nutty and wonderful. Watch them closely as they start to darken quickly at some point. Let them cool down completely before grinding them. 
4. Finely ground the walnuts in a food processor.
5. Sift flour, baking powder, and salt into a medium bowl.
6. Using an electric mixer, beat butter and sugar in a large bowl until light and fluffy, about 3 minutes.
7. Add eggs 1 at a time, beating well after each addition.
8. Mix in maple syrup, maple flavoring (if using), and vanilla extract. The batter may look curdled and will smooth out when adding the flour mixture.
9. Mix in the dry ingredients in 2 parts, using the mixer at the lowest speed.
10. Fold in the ground walnuts with a spatula and make sure the batter is thoroughly integrated.
11. Pour the batter into the prepared pan.
12. Bake until the top is golden, cracked, and a cake tester or toothpick inserted in the center comes out clean, about 1 hour. 
13. Transfer the pan to a wire rack and cool the cake for 20 minutes.
14. Make sure no batter is stuck to the sides of the pan. You can use a smooth-bladed knife to check the sides and around the center.
15. Carefully turn the cake out onto a cooling rack and cool completely before glazing. 
16. Drizzle the glaze (below) and let it drip down the sides. 
17. Place walnut halves on top and wait until it dries completely before cutting and serving. 
18. Store leftovers covered in plastic wrap for 2 days at room temperature and then refrigerate. 

For the glaze:

1. Mix powdered sugar with 2 tablespoons of maple syrup. 
2. Add more syrup until you have the consistency of thick honey. The glaze should be creamy and smooth. 
3. Keep refrigerated in an airtight container for a few weeks.