Method:
In a small skillet, melt butter over medium heat and sauté apples until softened, about 5 minutes. Add walnuts and cook for another 2 minutes. Remove from heat and set aside.
Whisk flour, brown sugar, baking powder, cinnamon, nutmeg and salt together in a large bowl. Make a well in the center of the dry ingredients. Whisk in milk and eggs until smooth. Stir in apple-walnut mixture.
Heat a large nonstick griddle or skillet over medium-high heat for 1 minute. Brush griddle lightly with butter. For each pancake, drop 1/4 cup of batter onto griddle, spacing pancakes apart. Cook until golden on bottom and bubbles start to form on surface, about 3 minutes. Turn pancakes over. Cook until golden on bottom, about 2 minutes longer. Repeat with remaining batter, brushing griddle with butter before each batch of pancakes.