Activate yeast mixture:

In a stand mixer bowl, stir together warm milk (110-115°F (45°C)), yeast, and sugar. Allow to rest for 5 minutes until foamy.

Knead dough:

Add warm water, whole wheat flour, 3 cups bread flour, shortening, honey, and salt. Using the dough hook on low speed, knead for 2 minutes, scraping the bowl as needed. Gradually incorporate up to 1/2 cup additional bread flour until the dough is soft and tacky but not sticky. Knead for another 2 minutes.

First rise:

Form the dough into a ball within the bowl, cover with plastic wrap and a clean towel. Let it rise in a warm spot for 1 hour until doubled in volume. (Optional: heat oven to its lowest setting for 1 minute, turn off, then place the bowl inside.)

Divide dough:

Transfer the dough to a lightly floured surface and knead for 1 minute. Split into 2 equal pieces.

Shape loaves:

Roll each piece into a rectangle, then fold into thirds like a letter, pressing the seams with the heel of your hand. Tuck the ends underneath and position seam-side down in two greased 9x5-inch loaf pans.

Second rise:

Loosely cover the pans with plastic wrap and let rise for 30 minutes.

Preheat oven:

Preheat the oven to 350°F (175°C).

Bake loaves:

Remove the plastic wrap. Brush the loaves with egg wash (1 egg whisked with 1 Tbsp water). Bake at 350°F (175°C) for about 30 minutes, until the internal temperature registers 190°F (90°C).

Brush with butter:

Optional: brush the tops with melted butter for a softer crust.

Cool loaves:

Cool in the pans for 10 minutes, then transfer to a wire rack. Allow to cool for at least 30 minutes before slicing.