A cookie-cutter has a sharp edge, to cut the cookie dough. (In memory of Mother.)

Draw a short line segment PERPENDICULAR to the two X curves, from the bottom inside corner, down to the outer curve, in a Green style (3D view is good for this).
In the Right View, highlight the green line segment, and draw a Red style polyline triangle downward, to a point.

In 3D view, sweep the triangle along the two X curves.
Boolean the two solids.

https://imgbox.com/YcwIEReg

The outer size of the Cookie is the "medial axis" of the Bottom View face of the X.

- Brian

Alternatively, the triangle could be internal to (a greater z height) X...

Of course, the cookies will then have a chamfered outer edge.
My memory of actual cookie cutters, is a thin band of metal, (possibly stamped), which is thin enough to count as a moderately sharp edge.
They had some sort of handle.