Mix herby olive oil: Combine 1 tablespoon olive oil, 1 tablespoon water, and 1 teaspoon chopped fresh herbs. Set aside while preparing dough.
Activate yeast: In a small bowl, stir together ½ cup warm water (105-115°F), yeast, and sugar. Let sit 5 minutes until foamy and bubbly.
Make dough: In a separate bowl, mix flour and salt. Add yeasty water and 1 tablespoon olive oil. Stir until sticky dough forms.
First rise: Cover bowl and let rise in warm spot for 30 minutes until dough increases in size.
Prepare pan: Generously oil a 9×7 inch baking pan with remaining olive oil, coating bottom and sides well.
Shape dough: Transfer dough to pan and gently stretch to fit. If dough resists, rest 5 minutes then continue stretching.
Second rise: Cover and let rise 30 more minutes until puffy and doubled in size.
Preheat oven: Heat oven to 400°F while dough completes second rise.
Dimple dough: Wet fingertips and press dimples all over dough surface, pressing down to pan bottom.
Add toppings: Drizzle herby olive oil over dough, letting it pool in dimples. Sprinkle with coarse salt and fresh rosemary.
Bake: Bake 15 minutes until golden brown and fragrant. Transfer to wire rack to cool slightly before serving.