In the US, it is often pronounced with the "sh" sound and is shown that way in dictionaries, as /grosh-re/. You can find many articles online arguing about how to say it. As a learner, I'd just pronounce it without the "sh", but be aware you will hear it that way. You will also hear it as both a two and three syllable word, but you should use the two syllable pronunciation.

there's no "shi“in it... it'sˈ'ɡrəʊs(ə)rɪ

In New York, it's normal to hear it pronounced "Gro/sh/ry," though I've heard "Gro/sry" often, as well. It doesn't matter, ultimately.

The 'sh' sound is the most common form spoken in my region, but I really feel that the difference is a regional thing. In some places it's with a 's' sound, others with a 'sh'. It doesn't really matter, but when pronounced with the 's' sound, the word's 3 syllable nature tends to come out rather than a 2 syllable sounding word using the 'sh;

I have never heard it with an "sh."