There are two ways to get a cookie cutter STL. Download one somebody else made, or generate one. Most people only try the first, spend forty minutes failing to find the right thing, and print something close enough.
This is an honest account of both, written by someone who did the first for about a year before building the second.
The places worth searching
Printables is the best of them. The models are mostly newer, the photos are usually of a real print rather than a render, and the comments will tell you if something does not work. Search "cookie cutter" plus your shape.
MakerWorld has grown quickly and the print profiles are genuinely useful if you have a Bambu. The cutter selection is thinner than Printables but the quality of what is there tends to be higher.
Thingiverse has the largest pile and the worst signal. Plenty of files from 2014 that were never printed by their author. The search is poor. It is still worth checking for unusual shapes, because if a thing exists anywhere it is probably there.
All three are free. None of them require an account to download, though Printables gives you points if you have one.
What is wrong with most of what you find
Four things, in the order they will bite you.
The blade is a wall, not a blade. A large number of shared cutters are an extrusion of an outline at a constant 1.2 or 2 mm. That does not cut cold dough, it presses it. A cutter needs to taper: thick at the base for strength, thin at the edge to cut. Ours goes 0.8 mm down to 0.4 mm, and when a cutter will not cut explains why that particular pair of numbers.
It is the wrong size and does not scale. You find a 60 mm cutter and you want 90 mm. Scaling it in the slicer scales the blade too, so the cutting edge goes from 0.4 mm to 0.6 mm and gets blunter. Scale it down and the blade drops under one nozzle width and will not print at all. Size and blade thickness should be independent, and in a shared STL they are welded together.
The detail is decorative, not printable. This is the big one for lettering. A name in a script font looks lovely on screen and has hairlines around 0.3 mm. Your printer cannot lay that down. Nothing in a downloaded STL warns you; you find out three hours in, when the letters lift off the plate in pieces.
The licence may not allow what you want. Most shared models are Creative Commons with a NonCommercial clause. If you are selling biscuits cut with it, read can you sell 3D printed cookie cutters before you list anything.
Checking a downloaded STL before you waste three hours
Slice it and look at two things.
Turn on the preview and check the blade is more than one line wide at the base and exactly one at the tip. If your slicer shows a gap where the blade should be, the wall is thinner than your nozzle and will not print.
Then look at the top layer of any lettering or fine detail. If a stroke disappears in the preview, it will disappear on the plate.
That two minute check saves the three hour print, and it is the same check whether the file came from Printables or from here.
When to stop searching
The rough rule: if you have spent longer than ten minutes looking, you will be faster generating it.
A plain shape somebody has definitely made, a star, a heart, a gingerbread person, is worth a quick search. Anything with a name on it, a specific character, a logo, a shape at a size nobody else needed, is not. Nobody has made a 92 mm cutter that says Amelia in Playfair Display, and nobody is going to.
Cutter Press generates the STL in your browser, free and without an account. Type the name, drop in the artwork, or pick from 169 built in shapes. The blade is tapered properly, the size is a number you set rather than a scale factor, and if the thinnest line in your design is under what your nozzle can lay down it tells you the measured width in millimetres and offers to fix it.
That last part is the actual reason this exists. Everything else you can get from Printables.