The pizza cutter’s handle made from, and how to stop it from staining everything it touches

Funny enough I was until recently working under a certified pizzaiolo. Are you allowing it to rest properly? How long are you kneading it for? What is your method for shaping your dough?

Edited to add from a later comment (I don't really see the point, it's right there after all):

Pizza dough, particularly if you are using proper 00 flour, needs a solid ten minutes of kneading before it rests. Resting time will vary depending on temperature and so on, but 2 hours seems excessive to me. Don't ever use a rolling pin to shape pizza dough; you've spent all that time working air into the dough, why squeeze it all out? Shape by hand, pulling towards you with your left while pushing away in a windshield wiper motion with your right and rotating the dough slightly on each pass.

I recommend starting with a chilled dough, puncturing with a knife or fork (see below), and cooking in a greased pan initially then bricking.

Cooking directly on the stone the entire time works better for thinner crusts than mid-dough. By mid-dough, I am referring to the ones that plump up a bit and finish between 1/4" - 1/2" in thickness. They can have both uniform, almost cake-y cross-sections, or air pockets and bubbles depending on how kneaded they are (more kneading means cake-ier, denser dough).

I worked in a shop that made a mid-dough similar to what you describe. It was a standard dough recipe (flour, water, yeast), but I have had success replicating it at home at 450'F with beer and less kneading. At home I use a pan and then finish either on the rack or a stone. In any case, you get a dough that tears nicely and has a good chew.

The dough itself was mixed in the morning and kept refrigerated for as long as 12 hours as individual shells in greased pizza pans covered with saran wrap. To prepare a pizza, we pulled the shell, punched it with a fork (puncture a ring around the edge to create a crust, puncture the inside to allow for air). Dress with sauce and toppings.

We had a stone-bottomed oven, but initially the pizza is baked in the oven in the pan until the bottom of the dough has hardened enough to get "bricked" (the dough should be rigid enough as to be removed from the pan with one spatula). At this point you remove the dough from the pan with a spatula and place it directly on the brick. Cook until the top of the dough browns, and the cheese and other toppings are evenly browned.