Pour the warm milk in the bowl of a stand mixer with dough hook attached or a large bowl is hand mixing/kneading. Add the sugar to the milk then sprinkle the yeast on the tops. Whisk the mixture and allow it to proof for 5-10 minutes. The mixture should appear foamy if yeast is active.
When you see the yeast is active, add the oil, flour and salt. Start at low speed with the dough hook on the mixer. When a ball starts to form (you may need a bit of additional flour), increase speed to medium and knead for 6-8 minutes on the machine, or 10-12 minutes kneading by hand. Dough should be soft and elastic yet not sticky.
Place dough in an oiled bowl, cover and let rise in a warm place until double in bulk; 1-1 1/2 hours.
After dough has doubled, punch it down to remove the air. Divide dough into 8 equal portions. Shape each into a ball and place 3 across, 3 down in a 9 x 9-inch greased square pan. Metal is preferred here. Cover and let rise until puffy--about 30 minutes.
Meanwhile, preheat oven to 350F/180C and make the herb oil.
Mix all herb oil ingredients in a small bowl and set aside.
When rolls are puffy, brush with the beaten egg and bake for 25-30 minutes; until they are a deep golden color.
Brush with the herb oil as soon as they are removed from the oven. Let them sit about 15 minutes to cool slightly before serving.