Preheat oven to 350ºF and line 2 8-inch greased cake pans with parchment paper rounds (see footnote); set aside.
In a mixing bowl, combine flour, baking powder, baking soda and salt. Whisk well and set aside.
In the bowl of a stand mixer, add butter and brown sugar. Using the paddle attachment, cream the ingredients on medium speed for 3 minutes.
While the appliance is running, add eggs, one at a time, mixing well between each addition; clean the sides and the bottom of the bowl when needed.
Add maple syrup and pure maple extract; mix for only 30 seconds.
Add half dry ingredients and process on low-speed until just combined.
Add the remaining half dry ingredients and the buttermilk. Process until just blended, cleaning the sides and the bottom of the bowl. Fold in the toasted walnuts.
Evenly divide the batter between the prepared cake pans and gently tap on the counter to dislodge any trapped air bubbles.
Transfer to the preheated oven and bake for 26 to 28 minutes or until a cake tester inserted in the center comes out clean with just a few crumbs.
Remove from the heat, transfer the cake to a wire rack and let them cool for 15 minutes before unmolding; allow to cool completely on the wire rack.