Learn Dutch: Dit is het lekkerste wat we hebben gegeten! - This is the tastiest thing we have eaten!

Because of a special rule for superlatives! When you have a neuter superlative acting as an abstract noun, like het lekkerste (the tastiest thing) or het beste (the best thing), Dutch requires the relative pronoun wat instead of dat.

Why is there no word for "thing" after het lekkerste?

In Dutch, you do not need to add a word for "thing". By taking the superlative adjective (lekkerst), adding an -e, and putting het in front of it, it turns into a noun meaning "the tastiest thing".

If I mention a specific food, like het gerecht (the dish), do I still use wat?

No, if you include a specific neuter noun, you go back to using dat. For example: Dit is het lekkerste gerecht dat we hebben gegeten (This is the tastiest dish that we have eaten). You only use wat when the superlative stands completely on its own as an abstract concept.

Why are the verbs hebben gegeten at the very end of the sentence?

The word wat introduces a relative clause, which follows subclause word order. This means the conjugated verb and any other verbs are pushed to the end. Note that you could also swap the final verbs and say wat we gegeten hebben—both orders are perfectly correct in Dutch!