Place the cream cheese in the bowl of an electric mixer fitted with the whisk attachment. Whip until smooth. With the mixer on low, slowly add the cream and then the scallions, dill, chives, lemon zest, lemon juice, salt, and pepper. Whisk until firm.
Line a 6-inch coeur a la creme mold or a 6-inch sieve with a few layers of cheesecloth, allowing the excess to drape over the sides. Pour the cream cheese mixture into the cheesecloth and smooth the top. Fold the excess cheesecloth over the top of the creme. Suspend the sieve over a small bowl, cover with plastic wrap, and refrigerate overnight.
When ready to serve, discard the liquid that has collected in the bowl and invert the creme onto a plate. Serve chilled with crackers and a small knife.