Prepare the Dough:

Dissolve sugar and yeast in warm water and let it sit until frothy, about 5-10 minutes.
In a large bowl, combine flour and salt. Add the yeast mixture and olive oil, and mix to form a dough.
Knead the dough on a floured surface until smooth, about 10 minutes. Place in an oiled bowl, cover, and let rise for 1-2 hours, until doubled.

Preheat the Oven:

Place a pizza stone or inverted baking sheet in the oven. Preheat to 500°F (260°C) for at least 30 minutes.

Prepare the Shrimp:

In a skillet, heat olive oil over medium heat. Add garlic and sauté until fragrant.
Add the shrimp, season with salt and pepper, and cook just until they start to turn pink (they will cook further in the oven). Remove from heat.

Assemble the Pizza:

Stretch the dough into a 12-inch circle on a floured surface or parchment paper.
Spread the pesto sauce evenly over the dough, leaving a border for the crust. Distribute the mozzarella cheese, then top with the partially cooked shrimp.

Bake the Pizza:

Transfer the pizza (on parchment if using) to the preheated stone or sheet. Bake for 10-12 minutes, until the crust is golden and cheese is bubbly.

Garnish and Serve:

Remove the pizza from the oven, garnish with fresh basil or arugula, and serve with lemon wedges on the side.