Preheat the oven to 400°F (205°C). Lightly coat all 12 wells of a standard muffin pan with neutral oil to prevent sticking.

In a large mixing bowl, thoroughly whisk together the all-purpose flour, whole-wheat flour, granulated sugar, baking powder, cinnamon, and salt. Continue mixing until the leavening and spices are evenly dispersed.

In a separate bowl or large measuring jug, whisk the egg, milk, and ½ cup neutral oil until the mixture is uniform and fully blended.

Pour the liquid mixture into the bowl containing the dry ingredients. Stir gently only until no large pockets of dry flour remain. A few small lumps are acceptable; excessive mixing may produce dense muffins.

Distribute the batter evenly among the 12 prepared muffin cups.

Spoon a portion of the pumpkin butter into the center of each filled cup. Using the tip of a knife or a toothpick, lightly draw the pumpkin butter through the surrounding batter to create a marbled appearance. Avoid excessive swirling so distinct pumpkin streaks remain visible.

Bake for 20 minutes, or until a tester inserted into the center of a muffin comes out clean.

Allow the muffins to rest in the pan for several minutes. Carefully remove them and place them on a wire rack to finish cooling.