Toast walnuts in the preheated oven until nuts turn golden brown and become fragrant, about 5 minutes. Watch carefully; nuts can burn quickly. Set aside to cool to room temperature.
Increase oven temperature to 375 degrees F (190 degrees C).
Place 3 tablespoons flour, 3 tablespoons brown sugar, and 1/2 cup cooled walnuts in a small bowl.
Cut in 2 tablespoons butter using two knives or a pastry blender until mixture resembles coarse crumbs.
Whisk together 2 cups flour, 2 tablespoons brown sugar, baking powder, and salt.
Cut in 1/2 cup butter using two knives or a pastry blender until mixture resembles fine crumbs. Stir in remaining 1/2 cup walnuts.
Whisk together 1/3 cup maple syrup and egg in a small bowl; stir into flour mixture. Gradually stir in just enough milk for the dough to leave the sides of the bowl and form a ball.
Place dough on a lightly floured surface.
Roll gently in flour to coat; knead lightly about 10 times. Pat into an 8-inch circle on an ungreased baking sheet.
Brush with milk; sprinkle evenly with topping. Score dough circle into 8 wedges with a knife, but do not separate wedges.
Bake in the preheated oven until golden brown, about 15 minutes.
Remove immediately from the baking sheet, and separate the scones.
