"Butcher shops" sell meat products, what is the name of a shop that sells cheese and ice cream?

Solution 1:

The closest suggestion I can think of is creamery.

creamery - Technically a manufacturing plant that processes cream, but can be used to describe a retail outlet. Example.

Consider also:

dairy (New Zealand English) - A convenience store. Sells milk, ice cream, newspapers, cigarettes etc.

Can you go to the dairy to pick up some milk?

delicatessen (often shortened to deli) - A shop selling delicacies, including fine cheeses, and less commonly ice cream, and also meats, salads, olives, etc.

Solution 2:

I've heard such a place called simply, "a dairy".

According to thefreedictionary.com, "dairy (n): 1. A commercial establishment for processing or selling milk and milk products."