Preheat oven to 400°F.
If preferred, on a medium skillet over medium heat toast the walnuts for a few minutes, keep and eye on them and stir frequently. Once the walnuts start getting brown remove them from heat and set aside to cool.
Prepare a muffin tin either by adding cupcake/muffin paper liners or by greasing the muffin cups with butter or baking nonstick cooking spray. Set aside.
In a large bowl, stir together: flour, baking powder, cinnamon, nutmeg and salt. Set aside.
In another bowl, combine eggs with sugar and oil, whisk to combine. Pause and add the milk and vanilla extract, whisk vigorously for 1 minute, until the mixture is fully combined.
Add the mashed purple yams to the egg mixture and beat until completely blended.
Using a spatula, stir in the flour mixture until just evenly combined.
Fold in the walnuts until just evenly distributed, no more than a few strokes to avoid overmixing.
Using an ice cream scoop, scoop the batter into the prepared muffin cups, filling them three-fourths full.
Sprinkle evenly with brown sugar and chopped walnuts, lightly pressing them into the batter.
Bake until the muffins are golden and springy to the touch. A toothpick inserted into the center comes out clean, 20 to 25 minutes. Start checking for doneness at 20 minutes.
Transfer the pan to a wire rack and let cool for 5 minutes. Unmold the muffins and you can serve them warm with butter or place them onto the wire rack to cool to room temperature so you can top them with the glaze.