Cacio e pepe attempt, how do I get rid of the small lumps of pecorino next time?

Tried to make a traditional cacio e pepe. What's the secret to a smooth emulsion between pasta water and pecorino?

I want a smooth sauce with no pecorino lumps. Did I let the pasta water cool too much or not mix well enough?

I bought a grated pecorino from whole foods and maybe it had something in it. The ingredients says: raw sheep's milk, rennet, salt, powdered cellulose.