Position a rack in the lower third of the oven, and preheat to 325 degrees F. Butter a 9-by-5-inch loaf pan.
Sift the flour and salt into a medium bowl. Whisk together the eggs, sour cream and vanilla in a small bowl.
Beat the butter in a large bowl with an electric mixer on medium-high speed until smooth. Gradually add the sugar, 1/4 cup at a time, to cream and lighten the butter.
Continue to beat the butter mixture until light and fluffy, about 5 minutes. Scrape down the bowl as needed.
Reduce the mixer speed to low. Beat in the flour, 1/4 cup at a time, then beat the batter for 30 seconds. Gradually beat in the egg mixture. (Take care not to overmix.)
Transfer about 1/3 of the batter to a medium bowl, and stir in the hot chocolate mix. Spoon 1/2 the remaining vanilla batter into the prepared loaf pan, and smooth over the top with a spatula. Using 1/2 the hot chocolate batter, drop spoonfuls on top of the vanilla batter. Repeat with the remaining vanilla and hot chocolate batters. Run a skewer through the loaf pan to help swirl the 2 batters together. Tap the pan on the counter.
Bake until a toothpick inserted in the center comes out clean and the top springs back when lightly pressed, 1 hour to 1 hour and 30 minutes.
Let the cake cool in the pan for a few minutes, then invert and let cool completely on a rack.
For best results, don't use hot chocolate or cocoa mixes that contain powdered milk or other dairy products, which can change the structure and texture of the cake.
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