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Preheat BBQ grill or stove-top grill pan to medium heat.
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Wash tomatoes and jalapeno, pat dry, then put them in a medium bowl. Drizzle with oil and toss to coat. Place vegetables on preheated grill. Grill for 10-15 minutes, turning 2 or 3 times, until tomatoes have softened, and both the tomatoes and jalapenos have black grill marks. Remove from grill and set aside until cool enough to handle.
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Quarter tomatoes, removing leaves and place in a blender or food processor. Remove jalapeno stem, seeds, and white-colored veins. (Unless you want this really spicy, then leave a bit in there.) Place jalapeno along with the remaining ingredients into the blender with the tomatoes. Process until smooth. Taste to check seasonings. If it's too acidic, add a little more sweetener and maybe a pinch of salt.
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Transfer to a sealed container (I like glass mason jars) and chill. Keeps in the fridge for about 2 weeks.
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Makes about a pint.
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Notes:
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1. To make salsa instead, omit the vinegar and oil and add the juice from one lime. Process until slightly chunky.
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2. If you aren't able to grill, you could roast the vegetables instead. Put them all on a rimmed baking sheet and broil, turning occasionally, until they get soft and black spots appear. I'm not sure how long it will take because I didn't do it this way, but I would estimate about 10-15 minutes.