The Uyghurs picked it up from Sogdian merchants and passed it on to the Mongols through trade. If you flip Mongolian script sideways it's easy to see the relationship to Syriac and Aramaic - it uses vowel markers like Aramaic and modern Arabic.
My favorite Mongolic script is Soyombo, which was based on Tibetan:
Powerlevel: I studied Mongolian for two years and never learned to read either. It's a total shitshow and learning it Cyrillic way was bad enough.
Try it yourself. You can learn the alphabet in one afternoon. Find a Korean toothpaste tube & you’ll be able to read it and understand some contextually important words - as some words are English derived as well.
(I know it sounds sort of stupid, but being able to read & understand real world text in a foreign language gives beginners the confidence & excitement they need to stick to their studies.)