Best answer: A Cobalt Mirror can be crafted from 50 Ionized Cobalt, but you'll first need to have its blueprint in order to do so.
Where to find Cobalt and Ionized Cobalt
Cobalt isn't exactly common, but it's not too hard to come across. When you're out in space just use your scanner on planets until you find one that lists Cobalt as one of its materials. This shouldn't take long as it can be found in almost every system. On the planet, Cobalt can be found in large deposits and can collected with a Terrain Manipulator. Ionized Cobalt can be found similarly through large crystals on planets with the use of an Advanced Mining Laser, but because it's rarer, the easiest method is collecting Cobalt and using a Refiner. Two Cobalt will yield one Ionized Cobalt.
Where to find blueprints
Blueprints can be found in Manufacturing Facilities on planets. Stay in your starship to blast the doors open because Sentinels will be guarding them. If you can't find a Manufacturing Facility, use a Signal Booster and search for Secured Frequencies. Blueprints are found at random, no there's no way to ensure that the one you get will be for a Cobalt Mirror. It's all dictated by the luck of the draw. Thankfully, once you find a blueprint you have it forever, so you'll be able to craft Cobalt Mirror without finding another so long as you have the ingredients.
Take to the stars
No Man's Sky is an ambitious space exploration sim from Hello Games. With the most recent updates, you can catalogue uncharted life on foreign worlds, build a home base with your friends and more. The sky isn't the limit anymore.
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Cobalt can be found on pretty much any planet that has caves. There might not be large deposits but there will be little pillar shadow minerals containing cobalt. Also if you mine those when your multi-tool is almost overheated you could get geodes that are worth around 20 cobalt after you analyse them.
This article is incorrect, signal boosters no longer function as described here, you need to turn your navigation data into the Cartographer in a space station. Operations Centres and manufacturing facilities give "Factory Override Units" for correctly solving the problem which can be spent on blueprints like the Cobalt mirrors or any of the other blueprints you previously would have gotten randomly. Recommend using the wiki which is updated by people who actually play the game, you'll get better information there.
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