phase changes take a lot of energy, but they're overestimating because ice doesn't completely melt when you shake a drink

1 gram ice absorbs 334J when it melts

3.5oz = 99.2 grams

so completely melting 3.5oz ice in 12s would absorb 99.2 * 334J / 12s = 2761 W

this is why those remarks about whiskey stones being useless are correct. most of the cooling effect of ice comes from it melting