Butter a 9-by-13-inch baking pan.

In a large pot, bring the water and whole milk to a boil. Add 2 teaspoons of Kosher salt. Slowly stream in the polenta, whisking constantly. Turn the heat down to medium-low, continue to simmer the polenta until thick, tender, and creamy, about 20 minutes.

Add the 4 tablespoons of butter and one-third of the Parmigiano cheese (⅔ cup), stir to melt in.

Quickly ladle 3 cups of the polenta (about half) into the prepared baking dish, evening out the top with a spatula. Refrigerate until firm.

Meanwhile, prepare the filling. In a heavy-duty skillet, bring 1-inch of salted water to a boil. Add the broccoli rabe or broccolini, cover, reduce the heat to medium and simmer, stirring occasionally, for 2-3 minutes until the broccoli rabe is bright green and only just barely tender.

Drain the broccoli rabe in a colander, running it under cold water to shock it and halt the cooking.

Using your hands, squeeze the leaves, wringing as much moisture as possible from the leaves as possible. Transfer the broccoli rabe to a food processor, pulsing several times to finely chop (or simply finely chop with a knife).

Wipe the heavy-duty skillet out to remove any moisture, add the olive oil and place over medium-high heat. Add the sausage, increasing the heat to high, and cook. While stirring, break the meat up with a spoon, until it is browned and cooked through, about 5 minutes.

Add the garlic to the skillet, continue sauteeing until fragrant and softened, about 1 minute.

Lower the heat to medium, add the chopped greens, cover and continue cooking, stirring occasionally to scrape up browned bits, until the greens no longer release water and are quite soft, about 7 minutes. Add another third (⅔ cup) of the Parmigiano, continue cooking until the cheese melts in. Remove from the heat.

Preheat the oven to 375 F.

Remove the pan from the refrigerator, cover the chilled polenta with half of the provolone slices in a single layer (you may need to tear some pieces to accomplish this). Spread the sausage and broccoli rabe filling on top of the provolone. Cover with the remaining half of the provolone slices.

Gently rewarm the remaining polenta, if necessary adding ¼ of water to loosen it. Spoon the warmed polenta on the provolone and even out the top with a spatula. Sprinkle the top with the final third of the Parmigiano.

Bake for 35 minutes, until the filling bubbles and the cheese on top is browned. Let the casserole rest for 10 minutes, then serve.