In a small saucepan combine 1 cup (227 g) milk, 1/2 cup (92 g) shortening, and 1/4 cup (57 g) water. Warm over low heat until the shortening is melted and the mixture reaches about 120°F (49°C). Remove from heat.
In a large mixing bowl, whisk together 1 1/2 cups of the 4 cups (480 g) flour, 1/3 cup (66 g) sugar, 2 teaspoons (5 g) kosher salt, and 2 1/4 teaspoons (7 g) active dry yeast.
Pour the warm liquid into the flour mixture. Beat with an electric mixer on medium speed for about 2 minutes until combined.
Add the remaining flour (the other 2 1/2 cups of the 4 cups total) and the 3 eggs to the bowl. Mix until a soft dough forms.
Turn the dough out onto a lightly floured surface and knead until smooth and elastic, about 5–8 minutes by hand (or 3–5 minutes using a dough hook on low speed). The dough should be soft and slightly tacky but pull away from the sides of the bowl.
Place the dough in a lightly greased bowl, cover with a clean cloth, and let rise in a warm, draft-free place until doubled in bulk, about 1 hour.
Grease a tube or Bundt pan well.
Punch down the risen dough to release air, press or shape it gently into the prepared pan so it is evenly distributed, and cover. Let the dough rise again in the pan until puffed and nearly doubled, about 30 minutes.
Meanwhile preheat the oven to 350°F (177°C).
Bake the bread at 350°F for about 40 minutes, or until the top is golden brown and a skewer inserted into the center comes out clean.
Remove the pan from the oven and let the bread cool in the pan for about 10 minutes. Then turn the loaf out onto a board or plate to finish cooling.
When cooled to a sliceable temperature, slice and serve.