Preheat oven to 425F and line a half sheet pan with parchment paper. Set aside.
Using a one cup glass measuring cup, heat water in microwave until an instant read digital food thermometer reads about 115°F. Pour the water into the bowl of your stand mixer measure the temperature of the water again and make sure it is about 110F, add in your sugar and yeast. Gently mix to combine.
Wait a few minutes for the yeast to activate you will notice it is getting foamy and starting to fluff up a bit in the mixing bowl. If your yeast does not activate because the water was not hot enough or too hot, start over.
Once the yeast has activated, add in your oil, sour cream and salt, and mix it well.
Lastly, add in your flour. Place the mixing bowl on the stand mixer and knead for about five minutes until it comes together to a smooth ball and passes the poke test. A.k.a. if you press your finger into it quickly, it should spring back where you pressed down.
Remove from mixing bowl and placed on a kitchen scale to weigh it out and divide your number into 10 to make 10 buns. Alternatively, you can just eyeball it.
I use a bench scraper and cut out the dough and wet on my kitchen scale to make sure they are pretty much even in size and weight.
Working quickly, flatten, one of the 10 pieces of dough and turn each corner of the dough into itself. Pinch the bottom together and if needed gently roll into a ball.
Repeat this process with the remaining dough.
Place each dough ball onto a parchment lined half sheet pan, cover with a clean kitchen towel and allow to rise for 10 to 15 minutes only. I place my pan close to the oven while the oven is preheating, so it is a nice and warm environment to rise in. If you notice the shape of the buns is more tall than it is wide, gently pat it down with the palm of your hand to flatten the shape into more of a hamburger bun look.
Make the fake egg wash
While your dough is rising, get a small bowl and combine the oil and milk. Stir it with your pastry brush and brush on the tops of the dough before the buns go in the oven.
Bake for about 10 to 12 minutes until the tops are nice and golden and the internal temperature reads at about 200°F.
Try to allow the buns to cool before cutting in half; if you need them quickly I have cut them after only 5 minutes out of the oven… and it still works fine!
Notes
⭐️I freeze any uneaten buns by wrapping each individual bun in plastic wrap, and then placing it into a Ziploc bag.