Bring the stock to the boil in a large saucepan and add the cabbage, cavolo nero and/or kale. Cook for a few minutes until softened (you may have to do this in 2 batches). Remove the cabbage to a large bowl with tongs or a slotted spoon, leaving the stock in the pan.
Toast all but 5 of the bread slices on a hot griddle pan or in a toaster, then rub them on 1 side with the garlic halves, and set aside.
Next, heat a large 4-inch-deep ovenproof casserole-type pan or Dutch oven on the stove top, pour in a couple of glugs of olive oil and add your pancetta and anchovies. When the pancetta is golden brown and sizzling, add the rosemary and cooked cabbage and toss to coat the greens in all the lovely flavors. Put the mixture and all the juices back into the large bowl.
Place 4 of the toasted slices in the casserole-type pan, in 1 layer. Spread over 1/3 of the cabbage leaves, sprinkle over a 1/4 of the grated fontina and Parmesan and add a drizzle of olive oil. Repeat this twice, but don't stress if your pan's only big enough to take two layers—that's fine. Just pour in all the juices remaining in the bowl and end with a layer of untoasted bread on top. Push down on the layers with your hands.
Pour the stock gently over the top until it just comes up to the top layer. Push down again and sprinkle over the remaining fontina and Parmesan. Add a good pinch of salt and pepper and drizzle over some good-quality olive oil. Bake in the preheated oven for around 30 minutes, or until crispy and golden on top.
When the soup is ready, taste the broth. If it has gotten a bit salty from the anchovies and cheese, add a little water till it tastes delicious to you. Divide it between your bowls. Melt the butter in a frying pan and quickly fry the sage leaves until they're just crisp and the butter is lightly golden (not burned!). Spoon a bit of the flavored butter and sage leaves over the soup and add another grating of Parmesan. Such a great combo!
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