Add half and half, pumpkin puree, confectioners sugar and spices in a pan, stirring everything to combine.
Heat gently, but do not bring to a boil.
Take pan off heat, and add vanilla. Cool slightly.
Using a fine mesh strainer, strain the mixture into a bowl. Discard solids.
Add brandy and stir to combine.
Using a funnel, pour into clean bottle(s).
For serving: In a bowl, combine graham cracker crumbs and pumpkin pie spice. Add 1/2 cup water to a separate bowl. Invert glass and dip in water, then dip in graham cracker mixture to line the rim of the glass. Pour punch over ice, and top with a splash of milk. Mix to combine and serve with a cocktail-sized straw.