Add half of the warm water (1/4 cup) to a large bowl with the yeast. The water should be approx 105 degrees Celsius (if you have a candy thermometer) or so warm it’s almost hot.
Let yeast and water sit for 10 minutes until proofed (the yeast forms a creamy foam on the surface of the water). Add in the following order (1) olive oil, (2) remaining 1/4 cup water, (3) salt. Stir with spatula to combine.
Add flour in 1/4 cup increments and keep stirring until it forms a sticky, loose dough.
Generously coat a 9-inch cast iron skillet (or metal baking pan) with olive oil. Add the dough and stretch out with your fingers so it fills the whole pan.
Cover the pan (using a plate or plastic wrap) and let rise in the oven with the oven light on until dough has doubled (approx 1 hr).
Take out of oven and press sliced tomatoes into the dough. Drizzle with approx 1 tsp of olive oil. Cover and let rise in the oven with the light on for an additional 30 min.
Sprinkle rosemary and another 1/2 tsp of olive oil on the dough. Bake for 20 minutes at 375. Rotate the pan halfway through cooking.
Let sit for 5 minutes before lifting bread out of pan and serving. Serve with olive oil and vinegar or use to make grilled vegetable sandwiches.