Still amazes me how the Persians invented a way to create and then store ice through the summer months for these treats.

https://en.wikipedia.org/wiki/Yakhch%C4%81l

Unfortunate how these traditional building methods for cooling have been replaced by loud and wasteful ACs etcs

Yep, but that, together with various similar and derived food, that both the Greeks and the Romans had, is more like sorbets.

The actual "cream" is thought to have been invented by Buontalenti:

https://en.wikipedia.org/wiki/Bernardo_Buontalenti

(eggs are needed to make "real" ice-cream):

https://www.florenceinferno.com/the-invention-of-ice-cream-i...

Only if you're going to "no true Scotsman" ice cream. For anyone not subscribing to that view, ice cream can be made with or without eggs. French style, Philadelphia style, Gelato, and churnless all differ in whether there are egg whites, egg yolks, cooked bases, and density.

One recent method is to use a Pacojet to take a hard-frozen solid block and turn it into ice cream.