Whisk 2 Tbsp. (16 g) bread flour and ½ cup water in a cold small skillet, preferably nonstick, until combined. Set over medium heat and cook, stirring constantly with a heatproof rubber spatula, until mixture thickens to the consistency of mayonnaise, about 2 minutes. Remove from heat; add 4 Tbsp. unsalted butter, cut into small pieces, and stir until butter melts. Transfer tangzhong to the bowl of a stand mixer.

Add 2 large eggs, ½ cup whole milk, ⅓ cup (60 g) nonfat dry milk powder, ¼ cup (50 g) granulated sugar, 2½ tsp. Diamond Crystal or 1½ tsp. Morton kosher salt, and one ¼-oz. envelope instant yeast (about 2¼ tsp.) to tangzhong; stir vigorously with spatula until eggs are incorporated. Fit stand mixer with dough hook; add 3 cups (375 g) bread flour and mix on low speed until a smooth, soft dough forms (it may stick to the bottom of the bowl but will mostly clear the sides), 20–25 minutes.

Transfer dough to a lightly dusted surface and shape into a ball. Lightly grease stand mixer bowl with vegetable oil. Return dough to bowl, cover tightly with a plate or plastic wrap, and let sit in a warm spot until nearly doubled in size, about 2 hours. (For optimal flavor, let the dough rise at room temperature 30 minutes, then chill overnight to proof slowly.)

Lightly coat a 9"-diameter cake pan with nonstick vegetable oil spray or unsalted butter. Line bottom with a parchment paper round; lightly coat parchment and sides of pan with more nonstick spray or butter. Mix ¾ cup (150 g) dark brown sugar, 4 Tbsp. unsalted butter, melted, slightly cooled, 3 Tbsp. instant vanilla pudding mix, 1 Tbsp. ground cinnamon, 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, and 2 Tbsp. room-temperature water in a medium bowl until smooth. (Filling should have the texture of hummus; if it feels runny, chill 5 minutes.)

Roll out dough on a surface lightly dusted with bread flour to about a 13x9" rectangle. Using an offset spatula, spread filling over dough in a thin, even layer, covering from edge to edge. Using a paring knife, cut dough lengthwise to create 3 strips of even width. Starting from long end of each strip, roll into a cylinder (like a jelly roll; you should have 3 long columns of dough).

Coil 1 column of dough, seam side up, in center of pan. Press down gently on coil to flatten slightly. Coil next strip of dough, seam side up, around first, followed by the third (strips should create an even round; the pan will be quite full). Press down gently on remaining 2 strips to flatten slightly. Cover pan loosely with plastic wrap and let sit in a warm spot until puffy (dough will not double in size), 45–90 minutes.

Place a rack in middle of oven; preheat to 350°. Remove plastic wrap from pan and bake cinnamon bun until golden brown, 20–25 minutes. Let cool.

Vigorously whisk 1 cup (110 g) powdered sugar, 2 oz. cream cheese, room temperature, 1 tsp. vanilla bean paste or vanilla extract, and remaining ¼ tsp. Diamond Crystal or Morton kosher salt in a medium bowl until very smooth. Transfer icing to a piping bag (or, use a resealable plastic bag and snip off a corner) and pipe over bun. Let sit 10 minutes for icing to set before serving.