Activate the yeast: Combine the warm milk, warm water, honey, and yeast in a small bowl. Let the mixture stand for about 5 minutes.
Mix the dough: Add the bread flour, rye flour, and salt to a large bowl. Pour in the yeast mixture, then add the egg and olive oil. Mix until a soft dough forms.
Knead the dough: Knead for about 8 minutes until the dough becomes smoother and more elastic. Keep the dough slightly soft instead of adding excessive flour.
First rise: Place the dough in a lightly oiled bowl, cover it, and let it rise for 60–90 minutes until noticeably puffy.
Divide the dough: Transfer the dough to a lightly floured surface and divide it into 8 equal portions.
Shape the buns: Shape each portion into a smooth ball, then gently flatten it with your palm to create a wider hamburger-bun shape.
Second rise: Cover the shaped buns and let them rise for 35–50 minutes until visibly puffy.
Prepare the topping: Mix the sesame, sunflower, pumpkin, and poppy seeds in a small bowl.
Add the seeds: Lightly brush each bun with milk or water, then sprinkle the mixed seeds evenly over the tops.
Bake the rye burger buns: Bake at 375°F (190°C) for 17–21 minutes, or until the buns are golden brown and firm on top.
Cool completely: Transfer the baked buns to a wire rack and allow them to cool completely before slicing.