Combine the flour and salt on a clean work surface and make a well in the centre. Crack the eggs into the well and add yolks. Use a fork to whisk, gradually whisking in the remaining flour from the sides. Use your hands to knead for 5 minutes or until smooth and elastic. Cover with plastic wrap and place in the fridge for 1 hour to rest.
Meanwhile, cook the kumara in a large saucepan of salted boiling water for 10 minutes or until tender. Drain well and transfer to a heatproof bowl. Mash until smooth. Add the parmesan and nutmeg and stir to combine. Taste and season with salt and pepper. Set aside to cool.
Divide pasta into 4 even portions. Flatten one portion to about 5mm thick. Dust lightly with flour. Set your pasta machine to the widest setting, then feed through the dough 4-5 times, folding in half each time and turning by 90 degrees. Continue feeding the dough through, without folding, narrowing the setting by 1 notch each time, until you reach the second-last setting. Arrange one-quarter of the sage leaves over one half of the dough and fold over to enclose leaves. Feed through pasta machine then fold and repeat one more time. Place on a lightly floured work surface and cover with plastic wrap. Continue in 3 more batches with remaining pasta and sage leaves.
Place rounded teaspoons of kumara mixture, 5cm apart in 2 rows on a pasta sheet. Brush around filling lightly with water. Place another pasta sheet on top and press gently around filling.
Use a 3cm-diameter pastry cutter to cut into rounds. Place on a tray dusted with flour. Repeat with remaining kumara mixture and pasta.
Cook ravioli in a large saucepan of boiling water for 2-3 minutes or until tender. Drain well. Meanwhile, melt the butter in a large frying pan over high heat until foaming. Cook, stirring, for 2 minutes or until butter turns a nutty colour. Add the pasta and gently toss until just combined. Spoon among serving plates. Top with shaved parmesan to serve.