A Tux-shaped cookie cutter generated from an STL file using Minkowski transforms.
The fundamental parametric OpenSCAD cookie cutter Thing (at http://www.thingiverse.com/thing:3060) shrinks the cookie shape to generate the wall outline, which works well for convex shapes. Unfortunately, Tux isn't convex and the shrinkage tends to wreck his crazy flipper feet.
So I started with a flat Tux-shaped slab created from Larry Ewing's Tux drawings (at http://www.isc.tamu.edu/~lewing/linux/) to get the cookie shape as an STL file, used OpenSCAD's Minkowski transforms to create the three wall thicknesses, stacked up the resulting layers, and punched out the central cookie shape.
This should work well for cookies with concave features slightly larger than the wall thickness, which you want anyway because cookie dough just doesn't render small details very well at all...
I used Inkscape to produce a DXF file, imported that into OpenSCAD to create the Tux slab, exported that as an STL file, then re-imported it into OpenSCAD to make the cutter. The current version of OpenSCAD has greatly improved DXF and STL import functions, so perhaps you can short-circuit the first part of the process.
A 6 minute annotated video of my Thing-O-Matic building a cutter, complete with a 30 second time-lapse overview of the whole process:
The backstory and more details: