Coffee Grounds and Gritty Butter Cream Icing Is there any way to dissolve coffee grinds once added to a butter cream frosting? 

I used instant coffee crystals in the past and they have always dissolved when simply added to the butter cream during the mixing stage — without having to dissolve in any sort of hot liquid prior to adding.

I have made this mocha butter cream frosting several times in the past, but didn’t think it through when I decided to use regular coffee instead of instant, which I discovered — albeit too late — that I was out of.
Instant coffee is "soluble solids of ground coffee" - ie, they made coffee, then they dried the result.

Actual ground coffee will never dissolve. 

When you make 'real' coffee you run/pour/pass water through the ground coffee, then throw away the solids. There's no getting around the 'throwing away' part.