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Preheat the oven to 300°F.
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Brush a baking pan with olive oil.
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Place the tomatoes, flesh side up.
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In a small bowl, dissolve the sugar in balsamic vinegar.
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Add garlic and 4 tablespoons of olive oil. Season with salt and pepper.
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Sprinkle mixture over tomatoes
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Roast for 2 hours at 275°F.
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At the end, to ensure the garlic is well roasted, change the setting to a broil for about 3-4 minutes.
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Allow to cool for about 1 hour; the tomatoes should be warm.
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Wash and pat dry the green beans.
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Heat the rest of the oil in a large, non-stick pan. Once the oil is hot, add the sliced onions and slowly cook until caramelized, stirring often.
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Add the beans. Toss well, leaving the heat at the highest setting for about 3 minutes until the color changes and becomes translucent.
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Add salt (this step will ensure a bright green color).
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Drizzle about 1 cup of water and cook until the liquid completely evaporates. The green beans should still be crisp at this point, not mushy.
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Adjust seasoning. Add more salt (if necessary) and pepper.
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Transfer to a platter and add the caramelized cherry tomatoes, drizzling the pan drippings over the greens. Toss well.
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Serve immediately.