Warm the milk to ~105–115 °F (40–45 °C). If using active dry yeast, stir the yeast and 1 tablespoon of the sugar into warm milk. Let it sit 5–10 min until foamy. (If using instant yeast, you can skip this proof-in-liquid step and mix directly with flour.)
In a separate bowl, whisk together softened butter, remaining sugar, and the egg. Then add the foamy milk (or warm milk if using instant yeast) and mix until combined.
In a large bowl (or stand mixer bowl), stir together flour and salt. Add the wet mixture. Mix until a rough dough forms.
Knead the dough on a lightly floured surface by hand for 8–10 min (or 5–7 min with a stand mixer dough hook) until the dough becomes smooth, elastic, and slightly tacky. Adjust with small amounts of flour or milk if needed.
Lightly oil a clean bowl, place the dough inside, turning once to coat. Cover with plastic wrap or a damp towel. Let rise in a warm, draft-free spot until doubled (~60–90 min).
After the first rise, gently deflate the dough and place on a floured surface. Divide into 12 equal pieces (≈ 60–70 g each). Shape each into a smooth ball. Place seam-side down in a greased 9×13-inch pan (or baking sheet), leaving space for expansion.
Cover and let the shaped rolls proof 30–45 min at room temperature until puffy and nearly doubled. Meanwhile preheat oven to 350 °F (175 °C).
Optional: Brush the tops with egg wash (egg + water) for a shiny golden crust — or milk for a softer top.
Bake for 15–22 min: smaller rolls ~15–17 min; larger rolls need more time. Bake until tops are golden brown and rolls sound hollow when tapped or internal temp ~190–200 °F (88–93 °C).
Immediately upon removing from oven, brush with melted butter or a honey-butter glaze to keep rolls soft and add flavour.