Step 1: In a medium saucepan, whisk together the granulated sugar and all-purpose flour until well combined.
Step 2: Slowly pour in the milk while whisking constantly to ensure there are no flour lumps.
Step 3: Place the saucepan over medium heat and cook, whisking continuously, until the mixture thickens into a heavy, pudding-like consistency.
Step 4: Remove from heat and stir in the salt. Transfer the mixture to a shallow bowl and cover with plastic wrap, pressing it directly onto the surface to prevent a skin from forming. Let it cool completely to room temperature.
Step 5: In a large mixing bowl, beat the room-temperature butter and vanilla extract with an electric mixer until light and fluffy (about 3-5 minutes).
Step 6: With the mixer on medium-high speed, add the cooled flour mixture one tablespoon at a time, beating well after each addition.
Step 7: Once all the flour mixture is incorporated, continue to beat the frosting for another 2-3 minutes until it looks like whipped cream and is smooth and glossy.