In a large mixing bowl, add the warm water, yeast, and honey. Stir to combine and set aside for 5 minutes.
Once the yeast mixture is foamy, add 1 cup flour and 2 tbsp. olive oil. Stir until the flour has been fully incorporated into the mixture. Allow to sit for another 5 minutes.
Stir in the last 1 cup of flour and 1/4 tsp. of salt. Once the dough has formed, transfer it onto a floured surface.
Knead the dough until it's smooth. The dough will be sticky in texture.
Then, oil a large bowl and place the dough inside. Cover with a lid or kitchen towl and allow to rise 1 hour.
While the dough is rising, prepare the infused oil. Heat 1/4 cup olive oil in a skillet over medium heat.
Add garlic, rosemary, salt and pepper. Cook, stirring, until the garlic has become fragrant, about 3-4 minutes. Remove from heat and set aside.
After the dough has risen for 1 hour, use some of the infused oil to coat an 8" round pan and preheat the oven to 450 degrees.
Place dough into pan and use your fingers to stretch it out. Then, dimple the dough.
Drizzle the dough with the infused oil mixture and top with roasted red peppers. Season with coarse salt and pepper.
Place a towel over the pan and allow the dough to rise 20 minutes. The dough will puff up a bit.
Then, bake in the oven for about 18-20 minutes, or until golden brown.
Carefully remove focaccia from pan and allow to cool on wire rack. Serve or store in plastic wrap at room temperature.