Preheat oven to 350°F. Grease a 9x5-inch loaf pan or line it with parchment paper.
In a medium bowl, whisk together flour, butterscotch pudding mix, baking powder, baking soda, and salt. Set aside.
In a large bowl, beat softened butter until creamy. Add eggs one at a time, then mix in vanilla extract.
Add the dry ingredients in batches, alternating with milk. Mix until just combined.
Pour batter into the prepared loaf pan and spread evenly.
Bake for 50–60 minutes, or until a toothpick inserted into the center comes out clean.
Cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
Whisk powdered sugar, milk, and vanilla together to make the glaze.
Drizzle glaze over cooled bread and sprinkle with butterscotch chips.
Slice and serve.