Soften the oats. In a small pot, heat the milk, 1/4 cup water, butter, and honey until the butter melts and the mixture is hot but not boiling. Stir in the oats. Remove from heat and let sit 10 minutes to soften and cool slightly. The mixture should be warm, not hot.

Proof the yeast. In a small bowl, mix the remaining 1/4 cup warm water (about 105–110°F) with the yeast. Let stand 5–10 minutes until foamy. If it doesn’t foam, your yeast may be inactive—start over with fresh yeast.

Build the dough. In a large mixing bowl, combine 3 1/2 cups flour and salt. Add the warm oat mixture, the egg, and the foamy yeast. Stir with a wooden spoon or dough hook until a shaggy dough forms.

Knead to smooth. Knead by hand on a lightly floured surface or in a stand mixer on medium-low for 6–8 minutes. Add flour 1 tablespoon at a time only if the dough is too sticky. You want a soft, slightly tacky dough that clears the sides of the bowl but clings a bit to the bottom.

First rise. Shape the dough into a ball and place it in a lightly oiled bowl, turning once to coat. Cover with a clean towel or plastic wrap. Let rise in a warm, draft-free spot until doubled, about 60–90 minutes.

Shape the rolls. Gently punch down the dough to release air. Turn out onto a lightly floured surface and divide into 12–16 equal pieces, depending on your preferred size. Shape each piece into a smooth ball by tucking edges under and rolling under your palm.

Pan and proof. Arrange the balls in a greased 9x13-inch baking dish or on a parchment-lined sheet, leaving a little space between them. Cover and let rise until puffy and touching, about 30–45 minutes.

Preheat and prep. While the rolls proof, preheat the oven to 375°F (190°C). Brush the tops with melted butter and, if you like, sprinkle a few oats or flaky salt on top.

Bake. Bake for 16–20 minutes, until the rolls are golden on top and sound hollow when tapped. If browning too quickly, tent loosely with foil for the last few minutes.

Finish and serve. Brush again with butter for a soft sheen. Let cool 10 minutes, then serve warm. They pull apart beautifully.