Position the rack in the center of the oven and preheat oven to 400°F To prepare the muffin tins, spray the indentions and the rims around them with nonstick spray or line the indentations with paper muffin cups. If using silicon muffin tins, spray as directed, then place them on a baking sheet.
Whisk the flour, sugar, pudding mix, baking powder, and salt in a medium bowl until uniform. Set aside.
In a large bowl, whisk the egg, milk, melted butter, and vanilla until light and smooth. Stir in the butterscotch chips with a wooden spoon, then quickly stir in the flour mixture until moistened.
Fill the prepared tins three quarters full. Use additional greased tins or small, ovensafe, greased ramekins for any leftover batter, or reserve the batter for a second baking. Bake for 20 minutes, or until muffins are well browned with smooth round tops. A toothpick inserted in the center of one muffin should come out with a few moist crumbs attached.
Set the pan on a wire rack to cool for 10 minutes . Gently tip each muffin to the side to make sure it isn't stuck. If it is, gently rock it back and forth to release it. Remove the muffins from the pan an cool them for 5 minutes more on the rack before serving. If storing or freezing, cool them completely before sealing in an airtight container or freezer safe plastic bags. The muffins will stay fresh for up to 2 days at room temperature or up to 2 months in the freezer.