Combine 2 cups milk and cream in a 4-quart kettle. A large kettle is important so the mixture does not boil over.
Add the sugar, corn syrup, and salt.
Place over medium-high to high heat and stir frequently so the mixture does not scorch.
While the mixture is heating, whisk the reserved 2 tablespoons of milk and cornstarch until dissolved. This creates a cornstarch slurry.
Bring the milk mixture to a boil. It seems wrong to boil the milk, but this works! Let the mixture boil well, stirring constantly for a few minutes.
After 2-3 minutes, remove from heat and whisk in the cornstarch slurry.
Once mixed in, place back on medium heat until the mixture just begins to bubble, letting you know the cornstarch has been activated.
Remove from heat and stir in vanilla paste and vanilla powder.
Let the mixture cool. Place in an airtight container and chill completely. I find overnight is best. When ready to freeze, remove from refrigerator and freeze using an ice cream maker. Follow the instructions with your maker. My KitchenAid stand mixer and ice cream attachment take about 25 minutes.
At this point, the ice cream is a soft-serve consistency. Place in a deep freeze to chill fully.
The vanilla powder is optional, but it does add an intense vanilla flavor.