In a 2 cup glass measuring cup, stir together warm water, 1 T brown sugar, and molasses or honey until well mixed. (If you need to warm it about 20 seconds more in the microwave to incorporate everything well, that's fine, just don't overheat to boiling, or it will be too hot for the yeast) Stir in the yeast and leave it to foam up for about 10 minutes.
Pour yeast mixture into the bowl of a stand mixer fitted with a dough hook. Add in the flours, 1/3 C brown sugar, salt, oil, and milk. Mix on low speed until it forms into a dough, adding more flour if necessary. Dough is done when it pulls away from the sides, and you can touch it without it sticking to your finger.
Place dough into a lightly oiled bowl, turning it once to coat. Cover and let it double in size, 1-2 hours depending on the temperature/humidity in your house.
Punch dough down and place on a floured surface. Divide into 2 equal portions and roll into two 16" x 8" rectangles.
Roll into loaves and pinch the seams together. Place loaves, seam side down, into greased loaf pans, tucking the ends under. Using a sharp knife, cut a few slits into the surface of the loaf.
Set aside to rise until it's about 1" over the sides of the pan, and when your finger leaves a dimple in the dough when touched, appx 30-45 minutes. If they don't seem to be rising fast enough (I've had this problem dependent on temperature), you can let them rise in a warm oven (170 degrees).
Preheat oven to 400. (If you had your bread rising in the oven, don't forget to remove before preheating) Bake for 12 minutes at 400, then, without opening the oven door, reduce heat to 350 and continue baking for an additional 20-30 minutes. Remove from pans and cool on wire racks. When done, loaves should sound hollow when you tap the bottom of the loaf.