Ensure egg whites are free from any trace of yolks and ideally at room temperature. Use a clean metal bowl free of fat or soap residue. Use an electric mixer to beat egg whites until stiff peaks form. If stiff peaks do not form, repeat with fresh egg whites and clean bowl.
Pour all milk except 1/3 cup (4 cups total) into medium-sized pot. Heat milk until just before it boils.
Make flour slurry: In a small bowl use a fork to stir together flour and reserved 1/3 cup of milk. Side aside.
In another small bowl stir together egg yolks, 1/3 cup sugar, and vanilla bean paste. Set aside.
When the milk starts to boil remove from heat, vigorously whisk in flour slurry to prevent clumping.
Temper the eggs: scoop out 1 cup of the hot milk mixture and very slowly drizzle milk into the egg mixture while vigorously whisking. This prevents the eggs from scrambling by gently warming them.
Once tempered add the egg mixture to hot milk in the pan while whisking.
Cook on low heat whisking frequently until it begins to set.
Add egg whites one scoop at a time and stir in completely before adding another scoop.
Once all is mixed in cook for 7-11 minutes, stirring frequently. The mixture should be quite thick.