Pulse the sugar in a mixie jar once or twice to make it super fine and keep aside.
Reserve 1/2 cup flour separately.
Grease a bowl with oil and keep it ready.
The butter should be cold and hard. Cut it into small cubes and keep it ready.
In a microwave safe bowl, mix together milk and vanilla essence and microwave at high for 30 secs. This heat would be perfect. You can also do this on stove top.
In a mixing bowl, mix together 1-1/2 cups flour, corn flour, yeast, salt and fine sugar.
Make a well in the center and pour the warm milk.
Spread your fingers and mix it together. It will become a big lumpy mass.
Add the cubed butter and work it into the dough.
The warmth of the milk and your hands are enough and it will easily merge with the dough. The dough will be sticky at this stage.
Add the remaining 1/2 cup flour and knead well for 4-5 minutes.
Place the dough in the greased bowl. Cover and let it rest for 1 hour or till it doubles in volume.
After an hour, gently deflate the dough by pressing the dough and letting the air out.
Dust your work area with flour and place dough on it. I used a shallow plate for this.
Using a rolling pin, roll the dough into 1/2 inch thick slab.
Using a donut cutter, cut out the shapes.
Gather the edges, once again, roll them and continue till all the dough is used up. I got only 3 dough holes at the end.
Transfer the cut donuts to a greased baking tray and arrange them side by side leaving enough space in between.
Cover with a thick cloth and let it rest for another 20 minutes. I just placed a big dinner plate upside down over the baking tray.
Preheat the oven at 200 C (400 F).
Bake for 10 minutes or till golden brown. Eggless baked donuts are ready.
Take the tray out and brush with melted butter all over the donuts. I just rubbed a hard cube of cold butter all over the top which did a better job. Let it cool for 5 minutes.