Make the dough: Heat milk, butter, 1⁄3 cup sugar, and salt in a 2-qt. saucepan over medium heat until sugar dissolves; set aside. Whisk together remaining sugar, yeast, and 1⁄4 cup water heated to 115° in the bowl of a stand mixer fitted with a dough hook; let sit until foamy, about 10 minutes. Whisk in milk mixture, add flour, and mix on low speed until dough forms. Increase speed to medium-high and knead until smooth, about 8 minutes. Cover bowl with plastic wrap; let sit until doubled in size, about 1 1⁄2 hours.
Meanwhile, make the filling: Heat oil in a 4-qt. saucepan over medium heat, and add bacon; cook, stirring, until fat renders, about 6 minutes. Add onion and cook, stirring, until onion is lightly caramelized but bacon is not crisp, about 6 minutes. Remove from heat; season with salt and pepper. Let cool completely.
Heat oven to 400°. Whisk together cream and egg yolk in a small bowl; set egg wash aside. Transfer dough to a floured work surface and cut in half. Working with one half at a time, roll dough until 1⁄4″ thick. Using a 2 1⁄2″ round cutter, cut out dough rounds. Place 1 heaping tsp. bacon filling in center of each round, and, using your fingers, moisten edges of round with egg white; fold over to enclose filling, and pinch edges together to seal. Transfer turnovers, seam side down, to parchment paper—lined baking sheets, spaced 3″ apart. Using a pastry brush, brush wash over each bun; bake until golden brown, 12–15 minutes.