Step 1
Mix 1/2 cup bread flour 1/4 cup water and sourdough discard together with a wooden spoon. Add a little flour to the bowl of a stand mixer. Add starter mixture and allow to rise in a warm area without direct sunlight until doubled in size about 2 hours.
Step 2
Attach dough hook and begin to mix the starter. Add remaining flour 3 tablespoons oil and 1 teaspoon salt. Mix in enough of the remaining water until dough pulls from the sides of the bowl and forms a ball; you may not need the full 3/4 cup. Knead dough in the mixer for 5 minutes.
Step 3
Transfer dough to a work surface and knead by hand for 5 minutes. Score and cover with a cloth. Allow to rise in a draft-free place until doubled in volume at least 2 hours and up to overnight.
Step 4
Lightly oil a shallow 12x16-inch baking pan. Knead dough for 5 minutes. Spread into the pan using your hands. Whisk 1 tablespoon oil and 1 tablespoon water together. Sprinkle a little bit over the focaccia. Cover with plastic wrap and let rise until doubled in height.
Step 5
Preheat the oven to 400 degrees F (200 degrees C).
Step 6
Push into the focaccia with your fingertips leaving indentations about 1 1/2 inches apart. Evenly distribute olives and cherry tomatoes on top pushing them into the dough. Sprinkle rosemary leaves and flaked salt on top. Sprinkle a little more of the oil-water mixture on top.
Step 7
Bake in the preheated oven until browned and cooked through 20 to 25 minutes. Drizzle olive oil on top before serving.