Cut bell peppers into fourths and place on a cookie sheet lined with foil, drizzle with extra-virgin olive oil. Roast 20 minutes. Remove bell peppers from the oven and immediately place in a large bowl covered with foil. Allow peppers to steam for 2 to 3 minutes. The peelings should easily come off once cooled. Discard peelings.
While bell peppers are roasting, add sun-dried tomatoes, along with oil from the jar, and garlic to a medium skillet, sauté on medium-low heat until tomatoes soften up, about 4 minutes. Add basil, toss just until wilted, remove from heat, drain oil and add vinegar, stir to combine. Cool 5 minutes.
Add cooled roasted bell peppers, black pepper and sun-dried tomato mixture to a food processor. Pulse until all ingredients are combined and sauce is a smooth consistency. Store sauce in a glass jar with lid in the refrigerator for up to two weeks.