Toddler tantrums over food.

[PeraltaSpidey]

My 14 month old is a very well fed little girl. However, she's started having food related full blown meltdowns and I don't know how to comfort her.
If she has a snack and she likes it, and she finishes it, the world absolutely ends. I can't just keep giving her more. For instance, today, she had an ice lolly. The last one. She ate the whole thing then absolutely screamed, slamming the packaging on the couch etc.

If I have something for myself, she screams the house down until I share it with her (which, obviously, isn't always possible). When I've finished (whether I've shared or not) she has a full on dramatic tantrum.
It's not because she's hungry. Like I say, she's very well fed. And if I can give her seconds, she'll scream if she finishes what she's eating no matter how much she's had. This doesn't usually happen with actual meals, just more "fun" snacks and things.
Is this normal development? What can I do to help her understand that food finishes?

A brisk 'All gone, well done' and immediately distract.

That's what I try. But "All gone" sometimes makes her worse! And she can't be distracted at that point. Literally nothing distracts her if she's so heightened.

Distract her by asking her to put her plate and spoon, or cup or lolly wrapping in the appropriate place. Lots of praise for doing that and being such a clever girl.
If you can’t distract her then try to ignore her, having a tantrum when no one reacts gets boring pretty quickly.