Activate the yeast: Add the whole milk to a bowl or liquid measuring cup. Microwave for about 1 minute or until the temperature reaches 100-110°F on a digital thermometer. It should be lukewarm and not too hot.
Whisk the granulated sugar, oil, and active dry yeast into the warm milk. Let that sit for 5-10 minutes to activate the yeast. It should start to foam on the surface if the yeast is alive.
Make the dough: Transfer the yeast mixture to a large bowl or the bowl of a stand mixer. Whisk in the honey, salt, and 2 cups of all-purpose flour.
Add 1 cup of whole wheat flour and mix it in with a wooden spoon or with the dough hook attachment in the stand mixer. Add more whole wheat flour, 2 tablespoons at a time, until the dough comes together and isn't too sticky.
Knead the dough: Knead the dough in the stand mixer with the dough hook attachment for 5 minutes. To knead by hand, turn the dough out onto a clean surface. Lightly dust your hands and the surface with flour if necessary. Fold the dough over itself towards you and then push it away with the palms of your hands. Turn 90 degrees and repeat. Knead the dough until it's smooth, elastic, and bounces back when gently pressed in.
First rise: Lightly grease a large bowl with oil or softened butter. Shape the dough into a smooth, round ball and place it in the greased bowl. Cover the bowl with plastic wrap or a slightly damp kitchen towel and let rise until doubled in size. In a warm environment this will take 60-90 minutes, but it can take several hours for the dough to rise (See notes for ways to speed up rising).
Lightly grease a 9x5" loaf pan with oil or softened butter. Once the dough has doubled in size, punch it down to release the air. Shape the dough into an oval shape and add it to the greased loaf pan.
Second rise: Cover the loaf pan with a slightly damp kitchen towel or plastic wrap and let rise again until doubled in size. Again, the dough will rise faster in a warm environment.
Bake: Preheat your oven to 375°F. Bake the honey wheat bread for 37-40 minutes. Cover the top loosely with aluminum foil halfway through to keep the top from browning too quickly.
Brush the top of the bread with melted butter and sprinkle with rolled oats, if desired.
Let the bread cool completely before slicing. Don't skip this step! I know it's tempting to slice into fresh-baked bread, but cooling is an important step in developing flavor and texture.