For the dough: Pour the warm water into a large bowl, add the yeast and sugar and stir to dissolve. Let sit until the yeast appears foamy, about 15 minutes. Add 2 cups flour, the salt and ajwain and stir with a fork until it comes together in a shaggy ball. Knead it a few times in the bowl to incorporate the flour on the sides of the bowl, and then turn it out onto a work surface. Continue to knead the dough for a few minutes, adding the 2 tablespoons flour if it seems wet and sticky. Do not add a lot of extra flour here as the dough should be very soft and pliable. Pour a little olive oil into a clean bowl and smear it around the edges. Rub it over the surface of the dough and then place the dough in the bowl. Cover with a towel and let rise in a warm place for 1 hour.
Preheat the oven to 425 degrees F.
For the pizza: Put the olive oil into a large skillet and add the onions, garlic and ginger. Saute until golden and soft, and then add the garam masala, turmeric, smoked paprika and salt and pepper. Add the spinach and stir until completely wilted. Let cool slightly, and then add to a food processor and puree until smooth.
When the dough is ready, pick it up and begin to stretch and pull it into a circle. Press it onto a pizza pan, stretching the dough to the edges. Spread the spinach mixture evenly over the entire pizza. Sprinkle the cilantro and green onions over it, and then add the tomato halves. Cover with the shredded cheese.
Place the pizza on the bottom rack of the oven and bake until the crust is golden and crispy and the cheese is bubbling, 25 to 30 minutes. Slice into wedges and serve.