Heat the milk, in a microwave, for 1 minute on high heat. Pour the milk into a large mixing bowl and add the vinegar, yeast and brown sugar; mix briefly. Let the mixture sit for 10 minutes to allow the yeast to proof, or grow.
Add the oil, honey and salt. Mix in the white whole wheat flour, 1/2 cup at a time, until the dough begins to pull away from the sides and remains slightly tacky. Knead for 5-10 minutes.
Cover the dough with a clean dish towel, and let it rise in a warm location for 1 1/2 hours; it should be at least double in size.
Remove the dough from the bowl onto a clean surface and roll the dough, with a rolling pin, the width of the loaf pan you will use to bake. Roll the dough up tightly and pinch the ends together at the seam. Tuck the 2 ends towards the seam. Place the dough, seam down, into a greased loaf pan.
Cover and rise again for 45 minutes-1 hour; until the dough fills the pan and doubles in size. While the dough is rising, preheat the oven to 350 degrees F.
Bake for 25 minutes using an aluminum foil tent. Remove the tent and bake an additional 10 minutes or until the internal temperature reaches 190 degrees F. Remove from pan and allow to cool on a cooling rack for 15 minutes. Slice and enjoy!