How to profile a logo?

In easel I’m going to carve this logo which I’ve done before. This time I would like to cut the wood as a profile or as close to the profile as I can get. What would be the procedure to complete this?

In Easel import the image using Image Trace.
Once its converted into a vector select the image and use the Shape Exploder App to break everything apart.
Once its broken apart select the profile of the image and any of the inside pieces, (I selected a box) then combine the two objects. The reason you need to select a piece from the inside is the profile image has an open path, once you combine it with something it will close the path and allow you to cut outside shape path.
Hope that makes sense