Place the blackberries in a medium bowl and roughly mash them with a potato masher. Stir in the jam, lemon juice and the 1/2 cup of the confectioners’ sugar; set aside.
 
In another bowl, stir together the peanut butter, cream and remaining 1/4 cup confectioners’ sugar.

 
Process the peanuts in a food processor until finely chopped. Transfer them to a large bowl.
 
Heat oil in a deep fryer or Dutch oven until the candy thermometer reads 350°F. Separate the biscuits. Working in batches, fry the dough, turning once, until deep golden brown and cooked through, about 2 minutes per side. Transfer to a plate lined with paper towels to drain for 1 minute. Roll the hot doughnuts in the crushed peanuts.
 
Using a chopstick or wooden skewer, poke a hole into the side of each doughnut, wiggling the chopstick from side to side to create a 1/4-inch hole. Transfer the peanut butter mixture to a large zip-top plastic freezer bag. Snip one corner off the bag. Pipe the peanut butter mixture into each doughnut until it almost bursts and the mixture begins to ooze from the side of the doughnut. Sprinkle the doughnuts with any remaining crushed peanuts. Serve with the jam mixture alongside for dipping.

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