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Add yeast and sugar to a mixing bowl. Pour warm water. (I heated mine in the microwave for 35 seconds). Let it stand for 10 minutes till the yeast froths and doubles.
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To this, add salt + oil + milk and mix well with a wooden spoon or a stand mixer fitted with dough hook attachment. Now add 2 and 1/2 cups of flour and mix well until a slightly sticky dough forms.
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Add the remaining 1/2 cup flour as needed until a slightly sticky dough forms. If you are not using a stand mixer, transfer the dough onto a floured surface and knead the remaining flour in with both the palms of you hand. (If the dough is very sticky, add a tablespoon or more flour as needed, but its good to have a slightly sticky dough rather than a dry one.)
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Coat the outer side of the dough with oil .Cover with a lightly damp kitchen towel and keep it aside for 1 and 1/2 to 2 hours or till the dough doubles in size.
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Prepare the garlic butter. Mix softened butter + salt + minced garlic (Don't mix the cheese) and keep aside. Grease and line a 9 inch cake pan, or a pie pan with parchment paper.
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Punch the dough, knead lightly and transfer into a lightly floured work surface. Lightly flour the rolling pin if needed. Roll into a 22 * 18 inch rectangle, about 1/4 inch thick. Spread the garlic butter evenly. Sprinkle the cheddar. Roll the longer side, jelly roll style.
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Cut the dough into half with a sharp knife or thread. Divide each side further into 2 and then divide that into 3 additional parts (This style ensures 12 even pieces).
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Arrange the pieces in the pan, cut side up. Cover the pan loosely with kitchen towel and let this rest for 30-45 minutes until it almost doubles.
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Preheat the oven to 375 Degrees Fahrenheit/190 Degrees Celsius. When the oven is preheating, brush the top and sides of the rolls generously with egg wash or milk. Sprinkle some more cheddar. Bake in the center rack of the oven for 25-30 minutes until the top is golden brown.
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Take this off the heat and place on a wire rack and brush additional butter for soft crust.