Combine butter, carrots, brown sugar, and salt in a saucepan over medium heat. Cook and stir until carrots are just getting tender, about 5 minutes. Season with cinnamon and ginger. Cook for 1 more minute. Turn off heat, and let cool.

Whisk together cream cheese, sweetened condensed milk, and vanilla extract in a bowl until smooth. Stir in cooled carrot mixture and transfer to the refrigerator until needed.

Beat cream in a chilled glass or metal bowl with an electric mixer until medium-stiff peaks form. Add cooled carrot-cream cheese mixture and whisk into the whipped cream. Fold in chopped walnuts and pecans with a spatula.