Make the Tangzhong: Whisk together milk and flour in a small saucepan until smooth. Cook over medium heat, whisking constantly, until a thick paste forms (like mashed potatoes), about 2–3 minutes. Scrape into a bowl and let cool completely before using (10–15 minutes).

Make the Dough & First Rise: In a stand mixer with a dough hook, combine flour, sugar, yeast, and salt. Add the milk, egg + yolk, and all the cooled tangzhong. Mix on low for 2–3 minutes until a shaggy dough forms. Increase to medium speed and mix for 5–6 minutes until the dough is firm, elastic, and tacky. Add the butter 1–2 tablespoons at a time, mixing until each addition is fully incorporated before adding the next. Scrape bowl/hook as needed. Once all butter is added, mix 7–10 minutes on medium speed until the dough is smooth, glossy, and can stretch thin without tearing (passes the windowpane test). Shape the dough into a ball and place in a lightly greased medium bowl. Cover with plastic wrap. Then, choose one of the following rise options: Same-Day (Faster): Let dough rise at room temperature for 1½ to 2 hours, until slightly puffy. Turn dough out and press into a flat rectangle. Wrap tightly in plastic wrap and freeze for about 30 minutes, until firm and well chilled (not frozen solid). Note: Do not freeze longer than 30 minutes — if you’re not ready to roll yet, transfer the dough to the refrigerator instead to prevent it from freezing through. Overnight (Preferred): Let dough rest (covered) at room temperature for 1 hour to kickstart fermentation. Then turn out the dough, press into a flat rectangle, wrap tightly in plastic wrap, and refrigerate overnight (8–24 hours).

Make the Chocolate Filling: Heat butter and cream in a saucepan over low until melted and steaming. Remove from heat and add chopped chocolate, ensuring it’s fully submerged. Let sit for 2 minutes, then stir until smooth. Whisk in cocoa powder, powdered sugar, salt, and vanilla until fully combined. Cool at room temp until thick and spreadable like frosting.

Shape & Second Rise: Line and grease an 8.5 x 4.5″ loaf pan with parchment paper, leaving a bit of overhang on the long sides for easy removal after baking. On a lightly floured surface, roll the chilled dough to an 11″ x 22″ rectangle (short side facing you). Spread chocolate filling evenly all the way to the edges. Then, roll up tightly from the short (11″) side into a log. Place log on a tray, cover, and chill for 20–30 minutes to firm up for clean slicing. Trim off ends with a sharp knife, then slice log lengthwise into two equal strands. With cut sides facing up, twist strands tightly together 3–4 times. Gently press and compact the twisted log to fit your loaf pan snugly. Transfer to the prepared pan. Cover and let rise in a warm spot for 1.5–2 hours, until puffy.

Bake: Preheat oven to 350°F (175°C). Bake for 50–55 minutes, placing the pan on a baking sheet. Tent with foil after 25–30 minutes to prevent over-browning. Internal temp should read 190–195°F (88–90°C). While baking, make the simple syrup, cooking the sugar and water in a small saucepan until sugar has dissolved. When the babka comes out of the oven, pour the syrup over it immediately while still hot — use all of it. Let the loaf cool completely in the pan before removing. Serve slightly warm. Wrap tightly once cooled and keep 2–3 days at room temp, or freeze for longer storage.