[Related by Abu Dawood, an-Nasaey and others authentically]
Now, does ice cream made with vanilla extract intoxicate? No one would say that. So, when does it become an intoxicant? If you extract the alcohol from that extract in the ice cream and isolate it, then it becomes an intoxicant and forbidden for consumption even if it is trivial in amount, because a large amount of the same substance would result in intoxication.
2 - Second, does mixing alcohol with food products make them impermissible or impure?
According to the stronger position (of the minority), alcohol is not physically impure. Thus, it doesn’t turn the mixture into impurity. Even, if it was impure, submersion in a large quantity of tahir (pure substance) according to the stronger position, does not affect the ruling of the pure substance unless one the characteristics of alcohol prevails (color, smell or taste).
Does mixing it with another substance change the ruling of the new substance even if it is not impure? Yes, if it makes the new substance an intoxicant.
3 - Third, would it be permissible for Muslims to add alcohol to food products? No - as in the case of turning alcohol into vinegar - that would not be permissible for Muslims, though, it would be permissible for them to consume it if it was added by others, and most certainly if it occurred naturally in a food (even bread goes through fermentation) so long as the consumed substance is not intoxicant, even in large quantities.
Based on what is said above, we believe that it is permissible to use food products which contain vanilla extract.
I hope this answer is satisfactory.
And Allah knows best.