Where does “набросить” come from?

набросить (Russian) comes from Russian на-, from Proto-Slavic na, from Proto-Indo-European h₂en- — on, onto.

Ancestry of “набросить”, step by step

Step	Language	Word	Meaning
1	Russian	на-	onto, upon; to repletion, to satiation, to the...
2	Proto-Slavic	na	on; concerning; onto
3	Proto-Indo-European	h₂en-	on, onto

набросить — Etymology, Origin & Word History | Etymology Explorer