Preheat oven to 400° F. On a lined baking sheet, toss your vegetables with enough oil to coat them well. Add a sprinkle of salt. Roast for 25-35 minutes, or until they're brown outside and soft in the middle, tossing halfway through. Set aside.
While your vegetables roast, Bring a large pot of well-salted water to a boil. (Taste it before you turn the heat on; it should be salty like the sea.) Cook your pasta until it's about 2 minutes from tender—it should be a little harder than al dente. Reserve 1/2 cup of pasta water. When the pasta is done, drain it.
While pasta is cooking, heat butter in a medium-large skillet over medium heat, until it froths. Add the pepper—this is the key! this makes its flavor "bloom"! and reminds you that pepper has its own unique punchy flavor and isn't just a culinary obligation!—and cook for a minute, swirling it around with your trusty wooden spoon.
Add 1/4 cup pasta water and bring to a simmer. Add pasta, and swirl it all around, and add 1/4 cup of cheese, and swirl it all around until it's melty. If it looks dry—you want it to glisten!—add a bit more pasta water.
Add the rest of the cheese and the roasted vegetables, and cook until the cheese is melted, everything is heated through, and the pasta is al dente.