Combine the warm water, 2 tbsp olive oil, yeast, and honey in a large bowl. Mix and rest for 5 minutes. Add the flour and salt and mix until a rough shaggy dough forms with no dry patches. Cover and rest for 30 minutes.
Wet your hands and grab one side of the dough, stretch upward and fold inward. Rotate and repeat on all four sides, scraping any dough off the edges. Cover and rest for 30 minutes. Repeat this stretch and fold process 3 more times with a 30 minute rest between each set.
Grease an 11x8 inch pan with 3 to 4 tbsp olive oil. Transfer the dough, fold the edges inward, and flip so the folds are at the bottom. Cover and rest for 1 to 2 hours until the dough has spread and puffed up.
Grind the basil leaves, olive oil, and flaky salt in a mortar and pestle until you have a vibrant green oil. Set aside.
Preheat the oven to 220°C. Gently stretch the dough to the edges of the pan if needed. Drizzle 1 to 2 tbsp olive oil over the surface and spoon the basil oil all over the top. Press firmly with your fingers all over to create deep dimples. Sprinkle generously with flaky sea salt.
Bake at 220°C for 20 to 25 minutes until the top is deep golden and the bottom is crispy.
Immediately brush with more basil oil and finish with a final scatter of flaky sea salt. Cool slightly before slicing.