I've made some custom cookie cutters which consist of two parts: the cutter and the stamp. First, you cut the outline of your cookie with a cutter and then use the stamp to imprint an image.

It was tricky to print the stamp part due to the large number of narrow lines. The specific setting will depend on your printer. I can only recommend experimenting with the "Minimum Wall Line Width" setting in Cura such that you can print thin lines without changing the width of all lines printed.

You should flour your dough and cutters generously, otherwise, they will stick. Also, it's easier to work with cold dough. I've used the following cookie recipe:

Ingredients:
1) Flour - 225 gr.
2) Sugar - 100 gr.
3) Vanilla Sugar - 25 gr. (optional)
4) Salt - 2 gr.
5) Egg - 1
6) Water - 1-2 tsp. (Just to help with the initial dough binding)
7) Butter - 112gr.

Mix all the ingredients, don't let the butter melt completely. Put it in the fridge to rest until cold. Roll the dough into the sheet and cut using the cookie cutter. Warm dough is sticky and hard to work with, so better to roll small portions, while the rest of the dough is in the fridge. After the cookies are cut, put them into the freezer for 15-20 minutes. While in the freezer, heat up the oven to 200-220 degrees. Bake for 12 minutes or until they become brown.