In a medium-size bowl, beat the cream cheese and the sugar till smooth. Add the egg and beat well. Add the flour and beat until incorporated. Set aside.
In a medium-sized saucepan over low heat, melt the butterscotch chips and the butter, stirring occasionally until smooth. Remove from heat and beat in the brown sugar until well blended. Allow to cool for 5 minutes.
Beat the eggs one at a time into the butterscotch mixture. Add the vanilla extract. Add the dry ingredients, beating until well combined. Stir in the walnuts. Pour the batter into the prepared pan.
Drop the cream cheese mixture by teaspoonfuls over the batter. Using a small knife, swirl the cream cheese into the batter, forming a decorative pattern.
Bake for 25-30 minutes or until a cake tester inserted into center of pan comes out with moist crumbs attached.
Do no overbake.
Allow to cook to room temperature, or overnight, before cutting and serving.