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Preheat the broiler. Place the bread on a baking sheet, brush the slices with 2 tablespoons of the olive oil, then broil until crispy. Turn over and toast the other sides.
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Turn off the oven, top the toasted bread with the cheese, and return to the still-warm oven to melt, but not brown.
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Top the cheese with the ham, peaches, a few grinds of pepper, the microgreens, and a drizzle of the remaining 1 tablespoon olive oil. Serve immediately.