For the bread: Heat the milk to between 110 and 115 degrees F. Dissolve the yeast in the warm milk.
Pour the milk mixture into the bowl of a stand mixer with a dough hook. Add the sugar, butter and salt and stir to dissolve. Add the rye flour and mix on medium until smooth. Slowly beat in the all-purpose flour. When the dough has come together, turn it out onto a lightly floured surface and knead it until smooth and elastic, about 5 minutes. Transfer the dough to an oiled bowl and turn to coat the surface. Cover with a towel and let rise in a warm place until doubled, about 1 hour.
Punch down the dough and place on a lightly floured board. Divide it in 2, knead each piece a couple of times and form them into rounds. Put the rounds on an oiled baking sheet, cover and let rise in a warm place until doubled, about 1 hour.
Preheat the oven to 350 degrees F.
Bake until the loaves are golden brown and sound hollow when tapped, 30 to 35 minutes. Remove to a rack to cool.
For the honey butter: While the bread is baking, put the butter, honey and just a dash of salt and pepper in a bowl and whisk it together. Scrape out into a ramekin and refrigerate. Remove from the refrigerator about a half hour before using.