Mash or press garlic; transfer to a large bowl. Whisk together 3 tablespoons balsamic, 2 teaspoons rosemary and 2 teaspoons thyme. Add mushrooms and radishes, toss well and set aside, tossing occasionally, for 30 minutes. In another bowl toss the remaining vinegar, rosemary and thyme. Halve the largest pieces of hearts of palm so you have at least 24 pieces; add to the bowl and toss to combine. Preheat oven to 425°F. Transfer mushrooms and radishes to a large, rimmed baking sheet lined with parchment paper and roast until softened and just caramelized, about 30 minutes. When cool enough to handle, thread a mushroom, piece of radish and piece of palm heart onto 24 6-inch skewers. Sprinkle with parsley and serve warm or at room temperature.
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