Add warm water and sugar together in the bowl of a stand mixer and stir. Sprinkle yeast over the mixture and let it sit for 10 minutes. It should be foamy after 10 minutes.
Add flour, olive oil, and sea salt to the yeast mixture. Turn mixer to low speed. Once the dough comes together, increase speed to medium-low and knead for 5 minutes. If dough is still sticky after 5 minutes, add 2 tablespoons of flour and continue to mix until combined. The dough should be easier to handle now.
Remove dough from mixing bowl and place into a large bowl greased with olive oil. Rotate dough in bowl to coat with olive oil. Cover with a damp towel and set aside to rise for 1 hour.
Preheat oven to 400 degrees. Punch down risen dough with your fist to remove the air pockets. Remove dough from bowl and place on 11x17 pan greased with olive oil (a 9x13 pan also works). Using your fingers, spread dough out to cover the entire bottom of each pan. Cover pan and let dough rise for 20 more minutes.
Once dough has risen, poke holes in dough with your fingertips. Spread dough with basil pesto and cover with sliced tomatoes. Finsih with a little more sea salt.
Bake loaf for 25-30 minutes or until top is golden brown and tomatoes have wrinkled. Remove from oven and let cool for 5 minutes. Remove loaves from pans and let them cool for a little longer before slicing and serving. Refrigerate any leftovers for up to 5 days.