Microwave the water for about 30 seconds, or until it reaches 110-115°F. It should be warm enough to activate the yeast, but not too hot, as high temperatures can kill it.
Combine the sugar and a packet of yeast, stirring well, and let it rest for 5 minutes.
In the meantime, mix the flour, baking powder, and salt. Then, add the beaten egg, vinegar, olive oil, and the yeast mixture with water.
Stir the mixture with a wooden spoon or rubber spatula until a dough starts to come together; it may still be a little sticky.
Cover the bowl with plastic wrap, then place a towel over it, and let the dough rise in a warm spot for 1 hour. The oven works well as a cozy place for this.
After the dough has risen for 1 hour, preheat the oven to 425°F. Place the dough in the fridge for 15 minutes to chill slightly, making it easier to roll out.
Transfer the dough onto a floured sheet of parchment paper and gently knead in 1-2 tablespoons of flour, just until it becomes a smooth ball.
Be careful not to add too much flour—just enough to make the dough less sticky and easy to handle.
Using a floured rolling pin, roll the dough into a rough 12-inch circle. I prefer a thicker crust, but if you like it thinner, you can stretch it out for a larger pizza or two smaller ones, depending on your preference.
Brush the top of the crust generously with olive oil and bake for 12 minutes.
Take the crust out of the oven, then add your sauce and desired toppings. Return it to the oven and bake for another 10-12 minutes.
If you like a crispier crust, bake it a bit longer; for a doughier texture, bake it a little less. Once it's done, let it cool for a few minutes before slicing and enjoying!