Preheat the oven to 350°F (175°C) and line a muffin tin with paper liners.
In a large bowl, whisk together the flour, granulated sugar, baking powder, salt, cinnamon, and nutmeg.
In another bowl, combine the melted butter, milk, eggs, and vanilla extract. Mix well.
Pour the wet ingredients into the dry ingredients and stir until just combined. Gently fold in the chopped nuts.
Divide the batter evenly among the muffin cups, filling each about 2/3 full.
Bake for 18-20 minutes, or until a toothpick inserted into the center comes out clean.
While the muffins are baking, prepare the honey syrup. In a small saucepan, combine honey, water, and brown sugar. Bring to a simmer over medium heat, stirring until the sugar dissolves. Remove from heat and let cool slightly.
Once the muffins are done, remove them from the oven and immediately brush the tops with the honey syrup. Allow the muffins to cool in the pan for 5 minutes before transferring them to a wire rack.
Serve warm or at room temperature.