In a small saucepan, heat the milk and fresh rosemary till just starting to produce steam (don't bring to a full boil). Turn off the heat immediately and set aside.
While the milk is heating, in a separate bowl, whisk together the 3 egg yolks, 3 tbsp sugar, 2 tbsp corn starch and 1 tsp vanilla till well mixed.
Once the milk is warmed, if you like you can strain the milk, so the rosemary bits get strained out. But I like to leave them in.
Slowly pour the warmed milk into the egg yolk base, whisking as you pour in a thin stream. Make sure to go slowly so it doesn't scramble the eggs.
Pour the mixture back into the saucepan and heat up again on medium. This time keep whisking as it comes to a boil.
The mixture will thicken up. Let it boil, while you keep stirring, for another few minutes to let the cornstarch flavour cook out.
Turn off the heat and pour into a heat proof dish (optional - for a smoother cream, strain the cream to get the rosemary bits and any lumps out. Personally I don't mind having the bits of rosemary in my cream). Place plastic wrap on top to prevent a film from forming. Cool to room temperature, then chill until ready to use.
The prepared rosemary cream will keep for a few days in the fridge.