In the bowl of a stand mixer, whisk together 1 cup (240 grams) room temperature water, Basil Pesto, and 1 tablespoon (15 grams) oil by hand. Add flour, yeast, and kosher salt. Using the paddle attachment, beat at low speed for 4 minutes; scrape sides of bowl. Switch to the dough hook attachment. Beat at medium-low speed until dough pulls away from sides of bowl and forms a smooth ball on dough hook, 2 to 3 minutes.
Oil a large bowl. Place dough in bowl. Cover and let rise in a warm, draft-free place (75°F/24°C) for 11⁄2 hours, folding dough in bowl every 30 minutes. (To fold, use wet or oiled hands to reach under one side of dough; gently stretch up, and fold over center. Repeat 3 more times around bowl.)
Brush a 10-inch cast-iron skillet with 1 tablespoon (14 grams) oil.
Turn out dough into prepared skillet, and using just your fingertips, gently stretch dough to completely fill skillet. (If dough is tight and will not stretch completely, let stand for 5 to 10 minutes and then try again.) Cover and let rise in a warm, draft- free place (75°F/24°C) for 30 minutes.
Uncover dough, and dimple with your fingertips, touching pan through dough without tearing dough. Cover and let rise in a warm, draft-free place (75°F/24°C) for 30 minutes.
Preheat oven to 450°F (230°C).
Uncover dough and gently dimple again. Drizzle with remaining 1 tablespoon (14 grams) oil. Sprinkle with sea salt.
Bake for 15 minutes. Reduce oven temperature to 425°F (220°C), and bake until deep golden brown and an instant- read thermometer inserted in center registers 205°F (96°C), about 10 minutes more, covering with foil to prevent excess browning, if necessary. Let cool in skillet for 10 minutes. Remove from skillet. Serve warm, or let cool completely on a wire rack. Serve with Basil Pesto. Best enjoyed same day.