In the small bowl, stir together boiling-hot water, cracked wheat or bulgur, and 1/2 teaspoon salt, then let stand until the grains are tender, about 40 minutes.
While grains soak, heat milk with butter in the small saucepan over low heat just until butter is melted.
In the bowl of the stand mixer, stir together the whole wheat flour, all-purpose flour, yeast, and salt. (If using active dry yeast, stir together yeast, warm water, and honey in a large bowl and let stand until foamy, about 5 minutes. If mixture doesn’t foam, start over with new yeast. Add flours and remaining 2-1/2 teaspoons salt to yeast mixture.)
Add the warm water and honey to the hot milk mixture. Drain bulgur in a sieve, then mix bulgur and milk mixture into flour mixture with the hook attachment on low speed (or a wooden spoon or rubber spatula if not using a mixer) until a sticky dough forms.
Continue mixing on 2 until the dough is elastic and almost smooth, about 5 minutes. (If not using a stand mixer, dust your work surface with flour and turn out the dough and knead, dusting surface and your hands with just enough flour to keep dough from sticking, until dough is elastic and almost smooth, 6 to 8 minutes.)
Form the dough into a ball. Put dough in a large oiled bowl and turn to coat. Cover bowl with plastic wrap and a kitchen towel and let dough rise in a draft-free place at warm room temperature until doubled, 2 to 2 1/2 hours.
Punch down dough (do not knead), then halve. Cover one half with plastic wrap. Cut the other half of dough into 12 equal pieces. Roll each piece into a 12-inch-long rope with floured hands (flour surface only if dough is sticky). Make a loop with each rope, wrapping it around fingers of one hand, then knot dough twice through loop, leaving 1 end in center on top and tucking bottom end under. Transfer to a baking sheet, arranging rolls 2 inches apart.
Repeat with the remaining dough, and place them on the second sheet. Cover rolls with a kitchen towel (not terry cloth) and let rise in a draft-free place at warm room temperature until doubled, 1 to 1-1/2 hours.
Preheat the oven to 375° F/190° C with racks in upper and lower thirds.
Brush rolls with egg wash and sprinkle with sea salt. Bake rolls, switching position of sheets halfway through, until golden brown, 20 to 25 minutes total. Transfer rolls to a rack to cool at least 20 minutes.
Rolls are best the day they’re made but can be frozen for 1 month. Allow the rolls to cool completely, then wrap well in plastic. Thaw, then reheat on a baking sheet in a 350°F oven until warmed through, 5 to 10 minutes.