There exists a position inside the earth where it is possible to cook a perfect pizza just by leaving it there

If you just leave it there it's likely to overcook. Take it out when it's done and enjoy.

Baking Bread with Lava in Iceland (actually with hot springs heated by lava)

There is this restaurant on a volcano on Lanzarote, in the "Parque Nacional de Timanfaya", where they cook with the heat from the magma below. I am sure you could cook a pizza with that, as well.

There are places on the planet Mercury that, if you were to find a lava tube of sufficient depth, would be the perfect temperature for human habitation. Some of the craters on Mercury's poles are never exposed to sunlight and actually have ice in them. Most of the planet is of course boiling hot when the Sun is overhead. But there should be some choice areas where you could skirt the balance of the two, and find lava tubes that, with proper sealing, would be quite comfortable for humans to occupy.

It's called a pizza oven!

Yeah. There is also likely a position in the earth where its possible to cook a human perfectly by getting them to bring a pizza there.

A pizza oven is about 450 C, so I'll figure it out based on this graph of the temperature in the Earth by depth.

0 to 500 C = 80 px
6.25 C per pixel
450/6.25 = 72 px

0 to 100 km = 54 px
1.85 km per pixel

Line y coordinate at 72 px x coordinate = 9 px
9*1.85 = ~17 km

The deepest hole we've ever actually drilled is the Kola superdeep borehole, which is a bit over 12 km deep. This is a fair bit short of our ideal pizza oven temperature, but it did see temperatures of 180 C, which is certainly enough to cook a pizza.

Probably, but is that position also accessible to you to put the pizza there in the first place, and be able to get it back out? Because if it isn't, all you've done is sacrifice a perfectly good pizza. ¯\_(ツ)_/¯

This would be a good question for What If (xkcd).

There was also a time when most of the universe was at the perfect temperature and density to cook pizza,I guess.

there are some spots on earth's surface where this is true as well.

You can probably find such a place on or close to the surface of the earth if it's close to an active volcano.

This is the place where the hidden ancient civilization of P'zz'r lives, a mystical forgotten place deep in the earth

Luckily, we can mathematically prove this with the Intermediate Value Theorem!

That is under my foot

There must be infinitely many such positions if there is one

Someone wants to summon Durin's Bane.

Only if temperature distribution is a continuous function.

Igneous extruded, is a type of pizza crust you'd get at a hipster pizza joint

People need to think about the crazy potential of geothermal energy in general. Thanks for bringing that up 🌋 . But the problem here: How do we get the Pizza down there 🍕. Folding the Pizza through a Borehole 🗼? How stable is the temperature at 100°C spots?

I think the process of transporting it there and back fucks with the temperature because the it increases and later decreases so slowly that it's overcooked just by bringing it there and back again.

What toppings? Are we talking fresh Moz? White sauce? This is very important.