In a saucepan over medium-low heat, combine the milk, sugar, and vanilla extract. Stir until the sugar is fully dissolved.
Let the mixture gently simmer (do not boil) for about 35 to 45 minutes, stirring occasionally, until it reduces by about half and thickens slightly.
Keep an eye on the mixture to prevent it from scorching or forming a skin on top.
Once thickened, remove from heat and let it cool completely; it will continue to thicken as it cools.
Transfer to an airtight container and store in the fridge for up to a week.