Heat oven to 375 degrees F. Lightly coat two 12-cup muffin tins with cooking spray and set aside.
Mix the softened cream cheese, 1 egg, and 3 tablespoons sugar into a small bowl and set aside.
Toss 5 tablespoons sugar, 1/2 cup flour, walnuts, butter, and 1/2 teaspoon pumpkin pie spice together in a medium bowl and set aside.
Combine the remaining sugar, flour, salt, baking powder, baking soda, and remaining pumpkin pie spice in a large bowl. Lightly beat the remaining eggs, pumpkin, oil, and vanilla together in a medium bowl. Make a well in the center of the flour mixture, pour the pumpkin mixture into the well, and mix with a fork just until moistened.
Evenly divide half the batter among the muffin cups. Next, place two teaspoonfuls of cream cheese filling in the center of each cup and fill with the remaining batter. Sprinkle some of the nut mixture over the top of each muffin and bake until golden and until a toothpick inserted into the muffin center comes out clean. Approximately 20 - 25 minutes.