Start by making sure your cream cheese is fully softened at room temperature before you begin. Cold cream cheese straight from the fridge tends to clump instead of blending smoothly into the rest of the mixture.
Add your heavy cream, softened cream cheese, pumpkin puree, brown sugar, pumpkin pie spice, vanilla, and salt into your mixing bowl or jar. Stir everything together briefly with a spatula before you start whipping, so the frother doesn't have to work as hard.
Use your milk frother or whisk to beat the mixture for about 30 to 45 seconds, until it turns thick, pale, and airy. You're looking for a texture similar to lightly whipped cream, not stiff peaks like you'd get with whipped topping.
Fill a tall glass with ice and pour in your cold brew or iced coffee, leaving a couple inches of room at the top. This is where the foam will sit once you add it.
Slowly spoon or pour the pumpkin cream cheese foam over your coffee, letting it float on top. Give it a light dusting of extra pumpkin pie spice if you want that classic café finish, then serve right away.