For the dough: In a large bowl or the bowl of a stand mixer fitted with the kneading hook, mix together 2 cups of the flour, the sugar, salt and instant yeast. In a measuring cup, combine the warm water with the oil. Add the water mixture to the dry ingredients and mix to combine. Knead by hand or with the mixer, add more flour in small increments, as needed, until the dough comes together into a smooth dough. It shouldn't stick to your hands or be dry and crumbly. Grease a bowl and place the dough ball into the bowl. Cover with plastic wrap and let rise until doubled, about 30 - 45 minutes, depending on how warm your kitchen is.
Prepare two baking sheets by lining each with a sheet of parchment paper. Set aside.
Remove the dough to a floured cutting board. Cut the dough evenly in half. Cut each half in half again. Cut each piece in half again and then in half again, to make a total of 16 roughly equal sized pieces.
Take a piece of dough. Form it in to a rough ball, then stretch in to a circle about 4-5 inches in diameter. (You don't need to stretch them completely at this point. Once the dough has rested a few minutes on the baking sheet, they will be easier to shape, so you will be going back and stretching them out a second time later.) Place the dough circle onto the prepared baking sheet. Repeat with each piece of dough, placing 8 on each on the prepared sheets (you can place them fairly close together as they don't spread much, but don't allow them to actually touch each other). Go back to the first pieces you formed and stretch them a little more, as needed.
With all your rolled dough on the baking sheets, using a teaspoon from your cutlery drawer, top each piece of dough with two heaping teaspoon of pizza sauce, spreading it over the top, going as far to the edges as you can without it going over the sides. Top with a generous amount of shredded cheddar cheese. Repeat with all the buns. Let stand 20 minutes, while you preheat the oven.
With racks in the upper and lower third of your oven, preheat oven to 375° F. with the rack in the centre of the oven. After buns have stood for 20 minutes or so (or until they look a little puffy around the outside edges), bake in preheated for 20-25 minutes , switching the pans from top to bottom half way through baking. Cook until well browned. Remove from oven and allow to cool on baking sheet for about 5 minutes, then remove to a cooling rack to cool completely. Enjoy immediately or cover and refrigerate. Or see below for freezing instructions!
Freezing: These buns freeze really well. Freeze them on baking sheet and then transfer to a freezer bag. To enjoy straight from the freezer, no need to thaw. Just place the frozen buns on a baking sheet and warm in a preheated 400° oven for 7 or 8 minutes.
Be sure to read the "Cook's Notes" in the original post, for more tips, options, substitutions and variations for this recipe!