In a large bowl with a handheld mixer or the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese and brown sugar until smooth. Add the molasses, ginger, cinnamon, nutmeg, and cloves and beat again on low until completely incorporated.
With the mixer on medium-high speed, add the heavy cream and beat until everything is combined and dip starts to get slightly fluffy (it will not fluff up like whipped cream). Chill in the refrigerator at least 1 hour before serving. Store leftovers covered tightly in the refrigerator up to 5 days.