First, preheat the oven to 350 degrees F. Line the muffin cups with paper muffin liners or grease with cooking spray.
Next, stir the flour, cinnamon, nutmeg, allspice, cloves, ginger, salt, and baking soda in a bowl.
Then, beat the brown sugar and eggs with an electric mixer in a large bowl until it is smooth. Add the 1/2 cup of oil and pumpkin, continue beating until mixed. Then pour the flour mixture into the egg mixture and beat until it is just incorporated.
Fill the muffin cups about halfway with the batter. Then spoon about 1 teaspoon of cream cheese into the center of the muffin cup, pushing it down into the middle of the batter. Sprinkle muffins with chopped walnuts.
Place the muffin pan in the oven and bake for about 22-25 minutes or until the tops spring back when lightly pressed. Or you can use a toothpick on the side of the muffin, it is done when it comes out clean. Allow the pan to cool for 5 minutes and remove to a rack to cool completely. The cream cheese stays hot for a while, so be careful and allow them to cool completely.