Sautee the onion and garlic: Get out a large pot, pour the 4 tablespoons of olive oil in it and place it over medium-high heat. Toss in the onion and sautee them for 5 minutes or until they become translucent. Then toss in the garlic and continue to saute for another minute.
Pour in the wine and use it to deglaze the pan.
Toss in the peppers, tomatoes, and tomato paste. Stir everything together.
Let it stew: Place a lid on the pot, and turn down the heat to low. Then let everything stew for 30 minutes making sure to stir everything a couple of times. Then take the lid off, and stir everything together again. Finally, let it continue to simmer without the lid for another 30 minutes, or until the peppers are as soft as you like.
Finish the peperonata by adding salt and pepper to taste, along with a few slivers of fresh basil leaves. Enjoy!