How to Make It
Preheat the oven to 425°. Rub the cut side of one squash half with 1 tablespoon of the olive oil, then sprinkle with a generous pinch each of salt and pepper. Set the squash half cut side down on a baking sheet and roast for 40 to 50 minutes, until tender. Scoop the flesh into a bowl and coarsely mash it.
In a medium saucepan, bring the water to a boil and whisk in the polenta. Bring to a simmer and cook over moderate heat, stirring occasionally, until soft and thick, about 20 minutes. Fold in the mashed squash and season with salt and pepper.
Meanwhile, peel the remaining squash half and cut it into 3/4-inch cubes. On a rimmed baking sheet, toss the squash cubes with the remaining 2 tablespoons of olive oil and 1/2 teaspoon of salt. Roast for 30 to 35 minutes, until tender. Remove and reduce the oven temperature to 400°.
In a small roasting pan, season the pork with 1/2 teaspoon of salt, then coat the meat with the mustard. Sprinkle the pork with 1/2 teaspoon of pepper and roast for 45 to 55 minutes, until an instant-read thermometer inserted in the center registers 120°. Transfer the roast to a cutting board and let stand for 20 minutes. Reduce the oven temperature to 325°.
Spread the hazelnuts in a pie pan and toast for about 10 minutes, until golden. Transfer to a towel and rub to remove the skins. In a mortar, pound the garlic to a paste with the sage and a pinch of salt. Add the hazelnuts and coarsely crush them in with the pestle.
In a medium skillet, cook the roasted squash cubes with the honey, vinegar and garlic over moderate heat until simmering; discard the garlic clove. Slice the pork between the ribs. Mound the polenta on plates and top with the pork chops. Spoon the squash cubes around the pork, sprinkle with the hazelnut picada and serve.