For the dough, combine the water, yeast, sugar and olive oil and let stand for 5 minutes until foamy. In a large bowl, mix together the flour and salt. Add the wet ingredients to the dry and stir until it forms a shaggy dough. Turn the dough onto a lightly floured work surface and knead for 10 minutes until the dough is smooth and elastic. (Alternatively, the dough can be mixed in the bowl of a stand mixer using a dough hook.)
Gather the dough into a ball, transfer to an oiled bowl and cover. Place the bowl in a warm spot to allow the dough to rise until it has doubled in size, about 2 hours.
For the pesto, finely chop the garlic in a food processor. Add the spinach, parsley, walnuts, Parmesan, salt and pepper, and process into a paste. While the food processor is running, pour the olive oil in a fine stream until the pesto is fully combined.
Preheat the oven to 450 degrees F with a pizza stone inside the oven.
On a lightly floured work surface, roll out the pizza dough into a 12-inch diameter circle. Sprinkle the preheated pizza stone with cornmeal and place the dough on it. Bake the crust for 5 minutes before spreading on the pesto, leaving a 1-inch border, followed by the artichokes and cheese. Continue baking for 5-7 minutes until the crust is golden brown and cooked through and the cheese has melted.
Sprinkle the pizza with red pepper flakes and parsley before serving.