Warm the water in the microwave to about 105 to 110℉. Add the warm water and yeast to a mixing bowl and let sit for 5 minutes.
Add the sugar, salt and 3 ½ cups of the flour to the mixing bowl. Mix until smooth.
Add egg and oil and mix until combined.
Switch to a dough hook if you have one. Add 3 more cups of flour and mix until the flour is fully worked in. The dough should be tacky but not too sticky. If it is very sticky, add a little of the remaining half cup of flour, two tablespoons at a time.
Spray a large bowl with cooking spray, add the dough, cover with plastic wrap and chill in the refrigerator overnight. If the dough rises too much, punch it down as needed.
About 2 hours before baking, remove the dough from the refrigerator. Shape into 24 equal size balls about 2 ounces each. You can eyeball this or divide the total dough weight by 24 and weigh each ball.
Spray a half sheet baking sheet with cooking spray, or spray two 9x13 pans. Place the 24 rolls on the half sheet or 12 rolls in each 9x13 pan.
Cover with a lightly floured tea towel and let rise for 1 ½ to 2 hours.
Preheat the oven to 400 ℉. Bake for 12-15 minutes until the tops are golden brown.
Optional: brush tops with dairy free butter while still warm and sprinkle salt or salt flakes on top.