Melt 2 tablespoons butter in a large skillet over medium heat. Add sausage; cook until well browned, about 3 minutes, breaking up meat with a wooden spoon. Add chopped onion; cook, stirring occasionally, until onion is soft and translucent, about 4 minutes. Add sage; cook, stirring occasionally, 1 minute more. Transfer to a medium bowl; season with pepper. Stir in cheese; set aside.
Melt remaining tablespoon butter in the skillet over medium heat. Add sliced onions; cook, stirring occasionally, until soft, about 4 minutes. Stir in cabbage, juniper berries, caraway seeds, bay leaf, verjus, and sugar, scraping bottom of skillet to loosen any browned bits. Reduce heat to low; cook, stirring occasionally, until cabbage is wilted and tender, about 10 minutes. Season with salt and pepper. Discard juniper berries and bay leaf.
Roll 3/4 of the dough on a lightly floured surface into a 21-by-12-inch rectangle, about 1/4-inch thick. Line a 13-by-4 1/2-inch loaf pan with dough, allowing dough to drape over edges. Freeze until cold, about 10 minutes.
Using an apple corer, remove 3/4 of the core from each pear, leaving stem end intact. Remove another tablespoon flesh from each cavity. Spoon 2 tablespoons sausage mixture into cavity of each pear; set aside.
Preheat oven to 375 degrees. Assemble pie: Spread cabbage mixture in an even layer over dough. Set stuffed pears on top. Roll out remaining dough on a lightly floured surface to a 14-by-6-inch rectangle, about 1/4-inch thick. Cut out four 2-inch circles from dough along centerline, about 1 inch apart. Place dough over pie, with pears poking through the holes. Gently crimp edges of dough to seal. Freeze until cold, about 15 minutes.
Whisk together cream and egg yolk in a small bowl. Brush crust with egg wash. Bake pie on a rimmed baking sheet until crust is golden brown and juices are bubbling, 45 to 50 minutes.
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