How Do I Replace Missing Craftsman Exterior Trim?

I recently purchased a 1934 home in Baltimore that features Craftsman details, including the trim that runs along the entire perimeter of the exterior of the house. It starts about four inches off the ground and wraps all the way around. The trim is a wide, flat piece of wood with another piece above it to create a lip on the top. That lip is 2 inches deep and 3/4 inch tall. The wide flat piece below that is about 9 inches in height. I don't really know how deep either piece is as they attach to the house's stucco exterior.

The problem I have is that there's one side of the house where the lip is missing. There is just a single flat piece of trim. The weird thing is that nowhere else on the house does it look like the lip on the top is attached to the flat piece. So maybe both pieces were removed and replaced with one taller flat piece without a lip?

Here are my questions:
Does this style of trim have a name?
How does it normally attach to the exterior wall?
Should I remove this flat piece to reinstall the lip?
What type of wood is used for this trim?

Thanks!

Our Answer

Thanks for the photos – they help me understand your situation better.
First, let's ID all these elements. I would refer to this trim as band board, and the lip as a sill. Both are normally secured to a foundation by nails or screws, and a waterproof seal should exist between the trim and the stucco. In layman terms, the water has to run down the stucco, strike the sill, and run OFF rather than behind the band board – similar to any type of flashing connection that stops absorption and leaks.
I wouldn’t, then, recommend adding the missing sill, because at this point it'll be difficult to restore any waterproofing integrity. Instead, I’d monitor the band board for signs of decay and rot. Trim is a common area for rot. Make sure to stay on top of painting and caulking it. And if you find yourself in a situation where you have to replace it because of rot or decay, use a pressure-treated lumber. This existing band board may have originally been a decay-resistant lumber like cedar, but you see how its integrity can be tainted when there's no waterproofing or flashing. For that reason, then, go with pressure-treated lumber moving forward.