Hello Nyagaki, Broccoli can do well in black cotton soil if:-
The soil is fertile, well aerated and drained and am sure this you can achieve by application of well decomposed FYM(Cow manure, Mbuzi's, chicken manure, composed manure etc)
Soil PH must be slightly acidic.(5-6.5)
soil temperature must most of the time be cool. Now biggest challenge hear is the color of your soil definitely it will absorb more heat from external environment so to manage this you will need to mulch using organic mulching materials as opposed to synthetic/plastic materials since the latter will require an efficient drip system.
Thanks