In a large liquid measuring cup, stir the beaten egg into the gently warmed milk. (Ensure the milk is warm to the touch, not hot, to avoid killing the yeast).

Stir in the 1 tablespoon of brown sugar and 1 tablespoon of cane sugar to feed the yeast.

Sprinkle the active dry yeast evenly over the top of the liquid and stir gently. Let the mixture rest undisturbed for 5 to 10 minutes until the yeast blooms and becomes highly frothy.

Place the melted butter, kosher salt, and the 2 ½ cups of bread flour into the bowl of an electric stand mixer fitted with a dough hook.

Pour the active, wet yeast mixture into the bowl. Mix on slow-to-medium speed until the flour and liquid are fully unified.

Gradually add the all-purpose flour, ½ cup at a time, steadily increasing the speed of the mixer. Stop adding flour when a soft, slightly sticky dough forms (about 5 minutes).

Once the dough wraps entirely around the hook and pulls away from the sides of the bowl, continue kneading on medium speed for 6 to 8 minutes until the dough forms a smooth, shiny, highly elastic ball.

Transfer the kneaded dough to a large ceramic or glass bowl that has been lightly coated with vegetable oil spray.

Cover the bowl tightly with plastic wrap and place it in a warm, draft-free environment (or a warming drawer set to the 'proof' setting) for 1 ½ hours, or until the dough has doubled in volume.

Generously coat two 8 ½ x 4 ½-inch metal loaf pans with vegetable oil spray. (Proper pan size is critical; oversized pans cause the dough to spread flat, undersized pans prevent cooking through the center).

Turn the proofed dough out onto a lightly floured work surface. Punch the dough down to deflate the gases and divide it evenly into two round halves.

Using a rolling pin, roll one half of the dough out into a large rectangle.

Brush the surface heavily with melted butter, then scatter an even, dense layer of brown sugar and cinnamon across the dough, leaving a ½-inch border around the edges.

Starting from the short end, roll the dough tightly into a firm cylinder. Pinch the seams closed and place the log, seam-side down, into the prepared loaf pan. Repeat with the second half of the dough.

Cover both pans loosely and allow the shaped loaves to rise in a warm place until doubled in volume, about 30 to 45 minutes.

Preheat the oven to 375°F.

Bake the proofed loaves on the center rack until the tops are deeply golden brown and the bread sounds hollow when tapped firmly on the bottom, about 30 to 40 minutes.

Remove the bread from the oven, immediately turn the loaves out of their pans, and allow them to cool completely on a wire rack before slicing to ensure the crumb sets perfectly.