This is how I easily made a custom cookie cutter with an embossed design.

Get your image. It needs to be black and white. The exterior black border will be what is cut out of the cookie, interior black details will be embossed. 

Here's mine:

Go to cookiecad.com and upload your design and select ‘Imprint Cutter’ (or whichever style you'd like). (I did not make and am not affiliated with cookiecad. I found them online after trying different image to cookie cutter tools and wanted to share them.)

Often that's all you have to do!

However my imprint has the cat's face floating unconnected to the cutter. You can sometimes use the center bars to connect those, but it wasn't able to cover my cat's full face. 

So in your favorite 3d modeler you can just add a simple block with the same height as your handle to connect everything. You can even just add it in your slicer.

Now absolutely any black and white image is available to you as a cookie cutter!!
 

I print in 100% infill just in case with cookie cutters.