Look for the plugin called 'SectionCutFace'
Its takes this:


And makes it look like this:


You can change the color of the 'fill'.
The other option is to go into your style settings and change the 'inside' color of a face to match the outside color. You'll still see the lines inside the timber - but the color will be the same (or better still, just change the default inside color black, to match the linework).