2 1/4 teaspoons (one 1/4-ounce envelope) active dry yeast
1/4 cup plus 2 tablespoons plus a pinch of granulated sugar
3/4 cup warm milk (110 degrees)
1 large egg plus 1 large egg yolk
3 cups all-purpose flour, plus more for surface
1 stick unsalted butter, room temperature, plus more for bowl, pan, and parchment
1 large egg, lightly beaten with 1 tablespoon heavy cream, for egg wash
1 1/2 cups pitted fresh or thawed frozen sour cherries
For the filling:
12 ounces softened cream cheese
1 large egg yolk
1/4 cup plus 2 tablespoons confectioners’ sugar
For the glaze:
1 cup confectioners’ sugar
2 tablespoons whole milk
Make the cake: Sprinkle yeast and a pinch of granulated sugar over milk in a medium bowl. Let stand until foamy, about 5 minutes.
Whisk together remaining 1/4 cup plus 2 tablespoons granulated sugar, the egg, and yolk. Whisk into yeast mixture.
Combine flour and 1/2 teaspoon salt in the bowl of a mixer. Add egg mixture. Beat on low speed until almost fully combined, about 30 seconds. Switch to the dough-hook attachment. Add butter. Beat until smooth, soft, and slightly sticky, about 10 minutes.
Butter a large bowl. Turn out dough onto a floured surface; knead a few times until smooth. Place in bowl, turn to coat, and cover with plastic wrap. Let stand in a warm place until doubled in volume, 1 to 1 1/2 hours.
Make the filling: Stir together cream cheese, egg yolk, and confectioners’ sugar.
Punch down dough. Transfer to a floured work surface. Let stand for 5 minutes. Roll out to an 18-inch square (about 1/8 inch thick). Brush edges with egg wash. Spread filling over dough. Top with cherries. Tightly roll dough like a jelly roll. Pinch seam to seal. Coil into a snail shape on a parchment-lined baking sheet. Brush top with egg wash.
Preheat oven to 350 degrees. Drape plastic wrap over dough. Let stand in a warm place until risen by half, 20 to 30 minutes.
Remove plastic wrap. Cut six 1/2-inch slits into top. Bake, rotating halfway through, until golden, about 55 minutes. Reduce oven temperature to 325 degrees. Bake until deeply golden, 15 to 20 minutes more (cover with foil if top gets too dark). Transfer pan to a wire rack. Let cake cool.
Make the glaze: Mix together confectioners’ sugar and milk. Drizzle over cake. Let set for 5 minutes before serving.