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1. Place peppers on hot side of grill and cook until blackened all over, 10-15 minutes. Transfer pepper to a large bowl, cover with plastic wrap, and let sit until cool enough to handle, about 20 minutes. Remove charred skin, seeds, and cores from peppers.
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2. While the peppers are cooling, pierce skin of eggplant with a fork all over. Place eggplant on cool side of grill. Cover and cook until skin darkens and wrinkles and eggplant is uniformly soft when pressed with tongs, about 30 minutes, turning halfway through for even cooking. Remove eggplant from grill and let sit until cool enough to handle, about 10 minutes. Trim top off eggplant and split lengthwise. Using a spoon, scoop out flesh of eggplant; discard skin.
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3. Place roasted red peppers, eggplant pulp, and garlic in a food processor fitted with a steel blade. Pulse until roughly chopped. Add in oil, vinegar, and salt and pulse until incorporated and peppers are finely chopped.
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4. Transfer sauce to a medium saucepan. Bring to a simmer over medium-high heat, then reduce heat to medium-low and simmer for 30 minutes, stirring occasionally. Remove from heat and season with salt and pepper to taste. Let cool to room temperature then use immediately or transfer to an airtight container and store in refrigerator for up to two weeks.
