Greetings - and welcome aboard!
Because its would be a "one-off" you could make a simple mold (PLUG) of the inside of the sink, its landing etc. The quality of the finish would be important - what you see - is what you get. The mold could be made of foam and hand sculpted to the shape - with all appropriate details.
Then, a coat to seal it - DURATEC has a good hard, glossy finish - don't know if you have it available. WAX it up, release agent etc.
Now, maybe a coat or two of surfacing resin sprayed on to get the gloss you'd be looking for - instead of gelcoat which tends to be pigmented and opaque.
When thats cured, start mixing up your stone and resin and lay it up over the mold. Mesh, roving, netting, wire etc could be used to support the slury of stone & resin.
You could apply some vacuum to hold to the shape and prevent sag too. Not to thick, several applications better than a thick one.
There are number of ways to do this - that's just off the top of my head how I'd approach it. You might try the Learning Center" at:
Sorry they are pdfs so won't babelfish for you. But the language is pretty straightforward. BTW your command of english reads pretty good to me
Good luck - Jim