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Grease the slow cooker insert with butter or vegetable oil. Cut a piece of waxed paper to fit the bottom and grease the waxed paper.
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In a bowl, beat the butter, eggs, sugars, and vanilla together until light and fluffy. In a separate bowl, stir the flour, baking soda, and salt together. Stir the dry ingredients into the butter mixture. Stir in the chocolate chips and walnuts until well blended.
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Spoon the dough evenly into the slow cooker and smooth the top. Cover and cook on low for about 3 hours, until a toothpick inserted into the center comes out clean. Set the lid slightly ajar for the last 30 minutes.
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Turn off the heat and remove the insert from the slow cooker. Allow to cool in the insert for 30 minutes. Invert onto a wire rack. Cut the cake in half lengthwise, then cut each piece crosswise into slices. Serve warm or at room temperature.
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note: This recipe was originally prepared in an oval, five-quart slow cooker.