Calendar Using Posts

I am working on a new site for a customer. They are not technically savvy, so I am trying to make posting content as easy as possible.

The client needs page displaying a text-based calendar of events for the year. They are not interested in a graphical calendar or a widget – they have requested a full calendar page sorted Jab-Dec. They would like it to appear similar to this:

January
01 – Event
[description]
10 – Event
[description]

February
15 – Event
[description]
20 – Event
[description]

…and so on.

Each event would be clickable. When clicked, you would be directed to a single post page with the event title and description.

Anyway, I can’t for the life of me figure out how to effectively do this in an organized manner.

I thought of creating a category for each month and then a sub-category for events, but I couldn’t figure out how to show that correctly on the calendar page.

I’m sure I am missing something.

Thanks in advance for any help offered.