Beat milk, sugar, egg yolks, and vanilla with a wire whisk in a saucepan; cook and stir over medium heat until beginning to thicken, about 5 minutes.
Fold the strawberries into the thickening mixture.
Whisk until the strawberries soften enough to nearly dissolve into the liquid. Continue cooking until nearing a boil and thick enough for a thin layer to cling to a spoon dipped into it, about 5 minutes.
Chill in refrigerator until completely cool.
Freeze in canister of ice cream maker according to manufacturer instructions.
