List an archive by year/month of a category

Hi everyone,

Something that I haven’t been able to find an answer to is this:

It is easy to add an archive to a blog so that when you select a month in the sidebar or wherever, you can see a list of posts for that month. I am assuming it is easy to also set up year headings to, so that the archive list looks like this:

2009
—-
January
February
March
.
.
.
December

2010
—-
January
.
.
.
December

BUT what I am having trouble with, is finding a way (without a plugin) to list an archive like the one above FOR 1 PARTICULAR CATEGORY only. For example, I would have a list of categories in my sidebar:

Cats
Dogs
Fish

Then when I clicked on Dogs, the main content page would load an archive of dogs category posts in a year/month list like so:

Dogs
—-
—-
2009
—-
January
– Post one
– Post two
February
– Post one
– Post two
.
.
.
December
-Post one

Does anyone know how I would go about this please? I think it would be a very useful task to be able to perform and service to provide for clients that want blogs that have excessive amounts of posts.

The reason I would like to know how to do this is because Archives are useful, however, if your blog has many posts, then a user, sorting through monthly archives looking for a post in the Fish category somewhere back in 2007 around summertime, would have trouble finding it. But with archives of categories, they would be able to narrow down their search easily by selecting the fish category first. After that is done, the user doesn’t have to search through all the posts from other categories, which could cut down their search by 50-90%.

Thank you for reading all this, I think clarity is better than quick illegible questions.