Start by making sure your cream cheese is fully softened at room temperature, since cold cream cheese will leave lumps in your filling. Beat it alone in a large bowl for about a minute until it's completely smooth and creamy. This step matters more than people think, because it sets the texture for the entire pie.
Pour in the sweetened condensed milk and beat it into the cream cheese until fully combined and glossy. Next, add the pumpkin puree along with the pumpkin pie spice, cinnamon, salt, and vanilla extract. Mix on medium speed until everything looks uniform in color with no visible streaks.
Using a rubber spatula, gently fold the whipped topping into the pumpkin mixture rather than stirring it in aggressively. This keeps the filling light and fluffy instead of dense. Fold just until you no longer see white streaks, scraping from the bottom of the bowl up and over.
Spoon the finished filling into your prepared graham cracker crust, smoothing the top with the back of a spoon or an offset spatula. Make sure the filling reaches the edges evenly so every slice looks clean when you cut it. At this point the pie will look soft, but that's completely normal.
Cover the pie loosely with plastic wrap and refrigerate it for at least 4 hours, though overnight gives the best texture. The cold is what firms up the filling, since there's no oven involved to set it. Don't rush this step, or your slices won't hold their shape.
Right before serving, top the pie with extra whipped cream, a light dusting of cinnamon, or crushed graham crackers. Slice with a clean, slightly warm knife for neat edges. Serve chilled straight from the refrigerator for the best flavor and texture.