Dissolve the yeast and sugar in 1 cup of warm water. Stir to combine and allow to sit for 5 to 7 minutes until mixture is fragrant and foamy.
In the bowl of a stand mixer fitted with a hook attachment, combine bread flour and salt. Add yeast mixture and remaining 3/4 cup of warm water. Mix on low speed for until dough is shaggy. Add olive oil and increasing mixing speed to medium. Mix until dough comes together and no longer sticks to the sides of the bowl. Stop the machine and cover mixing bowl with a kitchen towel. Allow the dough to rest for 10 minutes.
Remove the kitchen towel. At this point the dough will be very moist. Knead on medium-high speed for 2 minutes until dough is smooth. Place the dough in a well greased bowl. Cover and allow to rest at room temperature for 30 minutes.
While the dough is resting, toss together the cut tomatoes and fine sea salt. Place the tomatoes in a colander set over another bowl to allow excess moisture to drip out. Allow mixture to sit for 30 minutes.
Preheat oven to 425 degrees F. Line two 9x13-inch baking pans with parchment paper or a silicon mat. Generously grease the baking pans with about 1 Tablespoon of olive oil. Set aside.
Divide dough into two equal parts. Working with one dough at a time, transfer dough to greased baking pan. Drizzle about 2 teaspoons olive oil over top of dough. Use your fingers to dimple and spread out the dough to fit the baking pan. Repeat with remaining dough.
Place the drained tomatoes cut side up on dough. If desired, sprinkle grated parmesan cheese over dough. Season with salt, pepper, and crushed red pepper flakes. Cover with plastic wrap and allow dough to rest for 20 minutes.
Remove the plastic wrap. Bake the bread for 25 to 28 minutes until focaccia is golden in color and the internal temperature of bread registers at least 190 degrees F. Immediately out of the oven, brush tops of the focaccia bread with olive oil. Allow the focaccia to cool in the pan for 3 to 5 minutes before removing.
Use a serrated knife to slice the focaccia into individual portions. Serve focaccia warm or at room temperature.
Notes
Feel free to substitute other tomatoes in place of mini heirloom tomatoes, if desired.
Store leftover focaccia in the fridge. Bring to room temperature before eating, or warm up in a toaster oven or microwave.