Bloom the yeast. In the bowl of a stand mixer, whisk together the egg (1), sugar (1/4 cup), warm milk (2/3 cup), and yeast (2 1/4 teaspoons). Let it sit for 5 minutes until the yeast softens and looks foamy.
Mix + rest. Add the bread flour (2 1/2 cups) and salt (3/4 teaspoon). Using the dough hook, mix on low just until a shaggy dough forms. Cover and let rest 20 minutes.
Add butter + knead. Add the 2 tablespoons butter. Mix until incorporated, then knead on medium speed for 5–8 minutes. The dough should pull away from the sides of the bowl but stick to the bottom.
First rise. Cover and let rise about 2 hours, or until doubled.
Make the filling. In a small bowl, stir together the filling butter (1/4 cup), salt (1/4 teaspoon), sugar (1/3 cup), and cinnamon (2 teaspoons) until smooth and well combined. If using the optional Flavor Boost, mix it in now.
Prep the pan. Grease a 9×5 loaf pan or line with parchment.
Roll + fill. Turn the dough onto a lightly floured surface. Roll to about ½-inch thick. Spread the filling evenly over the dough.
Cut into 12 squares. Cut the dough in half lengthwise, then cut each half in half (4 rectangles). Cut each rectangle into thirds to make 12 squares.
Stack + arrange. Stack 3–4 squares at a time and stand them upright in the loaf pan. Repeat until filled. For the final stack, place the last square with the cinnamon side facing inward (plain side facing the pan).
Second rise. Cover and let rise 30–45 minutes, until puffy and the pan looks nicely filled.
Bake. Preheat oven to 375°F. If using egg wash, whisk egg (1) + water (1 tablespoon) and brush over the top. Bake 35–40 minutes until golden brown. If the top browns too quickly, tent with foil. (For best accuracy, the center should read 190°F.)
Glaze + serve. Whisk powdered sugar (1 cup) and milk (2 tablespoons) until smooth (add more milk if needed). Cool the loaf in the pan for 10 minutes, remove, drizzle with glaze, and pull apart to serve.