Bring a 6-quart / 5.5 L pot of water to a boil and season generously with coarse salt.

Add the potato cubes and cook for 5 minutes.

Add the sliced cabbage and cook 5 minutes more, until both are starting to soften.

Add the buckwheat pasta to the same pot. Cook according to package time, usually 10 to 12 minutes, until the pasta is tender and the vegetables are fully soft. If using fresh pizzoccheri, check earlier since they cook faster and turn mushy if left too long.

While the pasta cooks, melt the butter in a 10-inch / 26 cm skillet over medium heat with the smashed garlic and sage leaves.

Cook 3 to 4 minutes, swirling the pan often, until the butter turns golden brown and smells nutty. Remove from heat right away.

Warm the 9x13-inch / 23x33 cm baking dish by rinsing it with hot water and drying it, so the cheese doesn't seize when it hits a cold dish.

Reserve 1 cup / 240 ml of the pasta cooking water, then drain the pasta and vegetables in a colander.

Spread half the pasta mixture in the warmed dish. Scatter half the cubed Casera and half the Grana Padano over top. Repeat with the remaining pasta, cheese, and Grana.

Pour the hot sage butter evenly over the layers, garlic and sage leaves included if you like more punch, or removed for a milder flavor. Cover with a lid or foil for 2 to 3 minutes to let the cheese melt.

Toss everything gently with two forks until the cheese pulls into long strands and coats the pasta. Loosen with a splash of the reserved pasta water if it looks dry.

Season with black pepper and serve immediately, straight from the dish, family style.