Heat the saute pan and cook the onion in the olive oil with 1/4 teaspoon of the salt until it's soft, about 4 to 5 minutes. Drain the onions in the sieve over the medium bowl. Add the milk and stir.
In the bowl of the stand mixer, mix the all-purpose flour, rye flour, pepper, yeast, and the rest of the salt. (If using active dry yeast, stir together yeast, warm water, and honey in large bowl and let stand until foamy, about 5 minutes. If mixture doesn’t foam, start over with new yeast. Add flours and remaining salt to yeast mixture.)
Add the warm water and honey to the milk mixture, then pour into the dry ingredients. Mix on low until a soft dough forms. Turn the speed up to 2 and mix until the dough is smooth and elastic, up to 6 minutes. (To mix by hand, add the ingredients in order described to large mixing bowl. Stir with wood spoon until a soft dough forms. Turn the dough out onto a wooden surface that is lightly dusted with flour. Knead by hand until the dough is elastic and smooth, about 6 minutes.)
Add the onion and the chopped roasted walnuts, then mix again on low until everything is evenly distributed. (By hand: Pat the dough into a 9-inch square and sprinkle on the onions and walnuts. Fold the dough over to enclose the filling and pinch the edges to seal. Knead the dough to distribute the onions and walnuts throughout, about 2 minutes.) The dough will be lumpy. Push back in any pieces of onions or nuts that pop out, though this might be easier said than done.
Put the dough into a lightly oiled large mixing bowl and turn to coat. Cover the bowl with plastic wrap and a kitchen towel. Allow to rise in a draft-free spot at warm room temperature until doubled, about 1-1/2 to 2 hours.
Dust a work surface with flour. Punch down the dough, but do not knead. Divide in half and cover one half with plastic wrap. Roll the other half into a 12-inch (30.5 cm) log. Cut the log into 12 equal pieces and roll each piece into a ball. Place the rolls 2 inches (5 cm) apart on the prepared baking sheet. Cover with a tea towel. Make the rest of the rolls, place on the other baking sheet, and cover.
Allow the rolls to rise covered at warm room temperature until doubled, up to 90 minutes.
Place oven racks in the upper and lower thirds of the oven. Preheat to 375° F/190° C.
Brush the rolls with the egg wash and sprinkle with the poppy seeds. Bake for about 12 minutes, then rotate and switch the pans and bake for another 8 to 12 minutes, until golden brown.
Remove from the oven and allow to cool for 20 minutes on a wire rack, then serve.