A decent potion could revive this!

Depends on the stone. The coefficient of heat flow in stone is very low, so the heat will take forever to flow through the stone. But it should be quite evenly warmed at the top in a few hours if you keep feeding the fire. And it would be more or less immune to flare-ups and other issues.

However, you'd need to use a big slab of granite or something with more-or-less uniform properties, zero porosity (so no moisture or air bubbles are expanding or flashing to steam), and there's still a chance that fast heating or cooling causes it to crack.

Or just use a metal slab with a pizza stone on top.

It might blow up if there's the smallest amount of water in it.

In BoTW the cooking system is very open ended, you kind of just experiment with different ingredients and see if they work together. If they don't they make a plate of inedible food that actually damages your health and stamina. Pictured here is Gordon Ramsay, famous angry chef man, who is yelling at Link for making such a plate.