There are two ways to address this: using the standard view options, or creating a custom column.
By default, Outlook's View Settings allow you to change the way a field is displayed. This includes the most common formats for dates as well:
Sadly, you don't have full control over this. So using a custom format isn't possible here.
Custom Column (User-defined field)
The way to do this is to add a user-defined field. From the View Settings, go to Columns, New Column, set Type to Formula and then enter this formula:
Format([Received],"yyyy-mm-dd hh:mm dddd")
Obviously the string there represent your typical date format and offers you full control. Note that you can hit the Edit button to get a dedicated screen that offers quick ways to insert formulas and other fields. There's also a
Weekday() formula there but that returns the day of the week as an integer.
In order to change this column later, you'll need to remove the Column from the display so it's in the Available Columns list. You can then modify the formula with the Properties button on the lower left. Alternatively, and more intuitively, you can also edit the formula directly from the Format Columns menu now.
The biggest problem with this is that custom columns do not appear to support sorting. In my case I resolved this by creating a custom column just for the weekday and using one of the standard date formats for the Received column.
Both options look like this: