Preheat the oven to 350 degrees F, and butter a 9×13-inch baking dish.
In a large bowl, combine the milks, melted butter, eggs, and vanilla. Stir in the brown sugar and butterscotch chips, and then fold in the bread. Pour the mixture into the prepared baking dish.
Bake for 60-70 minutes, or until set. (We like crispy edges, so I bake on the longer side, covering loosely with foil once the top is sufficiently browned.) Serve warm, cold, or at room temperature. Covered tightly, leftovers will stay fresh in the refrigerator for up to one week.