You have probably heard similar sentences if you’ve ever lived in the UK. Indeed this particular use of ‘well’ is typically British and not common at all in American English.
WELL AS AN INTENSIFIER
In the above examples ‘well’ is used as an intensifier to mean ‘very‘ (‘that’s very interesting!’) or ‘fully‘ (‘I’m fully aware of the consequences’) with the aim of adding extra emphasis to what is being said.
When used as an intensifier, ‘very’ is followed by an adjective (interesting / aware).
Notice that this use is typical of colloquial and informal English. Don’t use it in formal writing!
a: ‘I’ve missed the bus by one minute and now I have to walk to work!’
b: ‘That’s well annoying!’
WELL AS AN ADVERB
Since we’re at it, it’s important to mention that in its most common use, ‘well’ falls into the category of adverbs like in the sentence ‘she can cook well’. In this instance, well is an adverb in that it describes the way an action (cook) is performed (well).
On a final note, ‘well’ can also be an adjective, that is a descriptive word, like in ‘I don’t feel very well’ or ‘I’m not well’.
So I hope that next time you hear someone using ‘well’ in this way it won’t puzzle you anymore.
I also suggest that you start using well as an intensifier every now and then, it will make you sound more ‘British’ 🙂