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1
Preheat oven to 325 degrees F (165 degrees C).
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2
Season roast generously on all sides with salt and black pepper.
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3
Heat olive oil in a large oven-proof skillet over medium-high heat. Cook roast in hot oil until browned on all sides, 3 to 4 minutes per side. Add shallot, cut-side down, to skillet and place rosemary sprigs on top of roast.
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4
Roast pork in the preheated oven for 45 minutes. Flip pork, place rosemary sprigs back on top of roast, and break up shallots with a spoon. Continue roasting until slightly pink in the center, about 45 minutes more. An instant-read thermometer inserted into the center should read at least 145 degrees F (63 degrees C).
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5
Transfer roast to a platter to rest for 10 minutes. Drizzle any excess fat in the skillet over the top of roast.
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6
Place the same skillet over medium heat. Stir blueberries into skillet and cook and stir until soft, 1 to 2 minutes. Pour port wine into the skillet and bring to a boil while scraping the browned bits of food off of the bottom of the pan with a wooden spoon.
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7
Stir chicken broth into blueberry mixture, increase heat to medium-high, and cook until liquid is reduced by half, 3 to 4 minutes. Reduce heat to low, stir cold butter into sauce and whisk until completely incorporated. Strain sauce through a fine-mesh sieve into a bowl.
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8
Slice pork roast against the grain into thin slices and top with blueberry sauce.
