In a bowl of a stand mixer fitted with a paddle, beat the cream cheese on medium speed until light and completely smooth, 4 to 5 minutes. Scrape down the sides of the bowl often, making sure all the cream cheese has incorporated and is silky smooth. Add the granulated sugar and beat on medium speed until completely incorporated, stopping to scrape down the bowl as needed, 2 to 3 minutes. Add the vanilla and salt, and beat on medium speed for 2 to 3 minutes. Add the eggs one at a time, beating on low speed after each addition until just combined. Using a spatula, give the filling a couple of turns to make sure it is fully mixed.