To brown the butter, cut it into tablespoons and place it in a medium skillet over medium heat. Melt the butter while swirling it in the pan occasionally. Be careful it will foam and pop. Once the butter starts to brown and smells nutty remove the pan from heat. There'll be small brown bits on the bottom of the pan and the butter should be an amber color. Pour the butter in a small bowl and let cool to room temperature.
Preheat the oven to 350°F (177°C) and line a 12-count muffin pan with muffin liners.
Remove the core of all apples. For the filling, grate one apple and mix with 2 tbsp of brown sugar and 1/2 tsp cinnamon. Set aside. Cut the other 2 apples into 12 rings. (You will get more than 12 rings, use the rings from the middle part of the apples)
In a medium bowl, combine all-purpose flour, baking powder, baking soda, 1/3 cup chopped nuts, 1 tsp cinnamon, and a pinch of salt. Set aside.
In a large bowl add the egg and give it a whisk. Add a 3/4 cup brown sugar, brown butter, and yogurt. Mix until well combined.
Add the flour mixture to the egg mixture but only stir until just combined. Don't overmix!
For the topping: In a small bowl combine 3 tbsp walnuts, 1 tbsp brown sugar, 2 tsp maple syrup, and 1/2 tsp cinnamon.
Fill 1/2 of the batter into the muffin cups. Divide the grated apple filling between the muffin cups and fill the cups up with the remaining batter.
Place an apple ring on top of each muffin cup and divide the topping between all muffin cups.
Bake for 20-25 minutes. Let the muffins rest in the form for 5 minutes then transfer to a cooling rack.