You can if the subject is clear from the context. For example, you might say, "I'm learning three languages at the moment, but English is my favourite".  In this case, it is understood that "my favourite" means "my favourite language".  

Or if you're looking at the standard selection of iced doughnuts at your local doughnut shop, you might ask tell your friend which one is your favourite (of all the varieties on offer).

Your example would only work if the subject has been mentioned. For example:

Question: "Do you have many hobbies?"

Answer:    "Yes, I do. But my favourite is learning English."

Here, it is understood that "my favourite" stands for "my favourite hobby".

There are also particular contexts where "favourite" is used as a noun. In families, "the favourite" is the child whom all the adults seem to like best, and in horse-racing "the favourite" is the horse which the bookmakers predict will win the race.

Then, of course, there's the award-winning film, "The Favourite", which was certainly among those most favoured at the recent Oscar ceremony.

You're welcome!