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To make the jam: In a small bowl, whisk together sugar, cornstarch, and salt. Place the sour cherries in a medium saucepan, add the sugar mixture, and toss to coat. Cook over medium heat, stirring often, until the cherries start to break down and release some of their juices, 3 to 5 minutes. Use a potato masher or pastry blender to crush the cherries (the mixture will still be quite chunky). Then let the mixture come to a simmer and cook, stirring frequently, until it has become thick and glossy, about 2 to 4 minutes. Transfer to a small bowl to cool, then stir in the vanilla.
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To make the dough: In a large bowl or the bowl of a stand mixer, combine the flour, brown sugar, baking powder, baking soda, and salt. Using an electric hand mixer or the flat beater of the stand mixer, beat in the butter until it’s evenly distributed, about 1 minute.
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In a small bowl or large measuring cup, whisk together the buttermilk, egg, and vanilla. Add the wet ingredients to the flour mixture and beat until just combined. It’s OK if you still see some dry flour.
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Transfer the dough to a lightly floured work surface and knead it until it forms a cohesive ball, about 30 seconds.
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On a floured piece of parchment, roll the dough into a 1/2" thick rectangle about 15" x 8"; pause periodically as you roll to pick up the dough (a bench knife is handy here) and sprinkle flour underneath as needed. Transfer the parchment to a baking sheet and chill for at least 20 minutes and up to 45 minutes.
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While the dough chills, preheat the oven to 375°F. Line a 9" square pan with a parchment sling, leaving a 2" overhang on two sides.
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Place a piece of parchment on your work surface. Remove the dough from the refrigerator and invert it onto the fresh parchment. Gently peel away the parchment from the top.
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Scoop out 1/4 cup (70g) of the cherry jam and set it aside. Spread the remaining 3/4 cup (210g) of the sour cherry jam evenly over the dough with an offset spatula, leaving a 1" bare border on the side farthest from you.
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Roll the dough into a spiral, starting from the long side nearest you and working towards the bare border. Use a serrated knife to cut the log lengthwise into three 5" pieces, then cut each piece in thirds to make a total of 9 cherry buns. Gently place the pieces in the prepared pan, cut side up. (A bench knife will help with neat transfer.)
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Bake the cherry buns for 26 to 28 minutes, until puffed and light golden. Let cool for 5 to 10 minutes while you make the frosting.
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To make the frosting: In a large bowl, use a wooden spoon or flexible spatula to beat together the cream cheese and confectioners’ sugar until smooth. Add the reserved sour cherry jam and the pinch of salt and stir to combine. Spread frosting over the warm buns and serve immediately or let cool to room temperature.
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Storage information: These cherry buns are best the day they’re made. Store any leftovers covered at room temperature for up to 1 day.
