Preheat oven to 425 degrees F.
Make the pizza dough. Combine the warm water with yeast and sugar. Let sit for 5 minutes or until the yeast is activated and the mixture is foamy.
Combine the yeast mixture with the flour, salt, and olive oil, mixing until a dough forms. Knead the dough until smooth, about 5 minutes. Lightly oil a clean bowl and place the dough in the bowl. Cover and let rise in a warm area until doubled in size, about 1 hour.
Meanwhile, prepare the roasted pepper sauce. Toss the onion half and garlic cloves with 1 tablespoon oil. Lay the onion, garlic, and bell peppers on a sheet tray and roast in the oven for 25 minutes, flipping the vegetables over halfway through. Remove from the oven and place the bell peppers in a bowl. Cover with plastic wrap and let sit for 10 minutes.
When the peppers are cool enough to handle, peel off the skin and remove the seeds. Remove the skin from the onion and garlic cloves. Place all of the roasted vegetables in a blender along with tomato paste, fresh basil, oregano, fennel, salt and pepper and puree until smooth. Set aside.
Increase the oven temperature to 450 degrees F. Line a 9x13 inch baking sheet with parchment paper.
Punch down the dough. Lightly flour the lined baking sheet and place the dough on top. Stretch out the dough with your hands until it fits the baking sheet, making sure the dough is even throughout. Spread the roasted pepper sauce on top in an even layer. Top the pizza with fresh mozzarella, pepperoni, cherry tomatoes, red onion, and jalapeno. Bake the pizza in the oven for 15 minutes or until the cheese is melted and lightly charred.
Remove the pizza from the oven and top with fresh basil. Serve immediately.