Mix the buckwheat flour and unbleached flour. Add eggs, milk, water, and salt and knead into a pasta dough.
Roll the dough thicker than for fettuccine. Let it dry briefly so it will cut cleanly without cracking.
Fold loosely and cut into 1-inch (2.5 cm) ribbons, then cut each ribbon diagonally to make diamond-shaped noodles about 3 to 3 1/2 inches (8 to 9 cm) long. Spread on cloth towels.
Preheat the oven to 400 F (205 C).
Wash the chard stalks.
Boil 4 quarts (3.8 L) water, add 2 tbsp salt, add the chard, and cook 10 minutes. Add the potatoes and continue until both are tender.
While they cook, heat the butter with the mashed garlic over medium heat until the garlic turns light nut-brown. Discard the garlic, add the sage leaves, turn them once or twice, then remove from heat.
Butter the baking dish.
When chard and potatoes are tender, drop the noodles into the same pot. Cook the noodles until slightly underdone and very firm to the bite, then drain noodles, chard, and potatoes together and transfer to the baking dish.
Pour over the sage butter and toss well.
Mix in fontina and Parmesan, level the dish, and bake on the top rack 5 minutes. Rest 2 to 3 minutes, then serve from the dish.
