Place the orange juice and lemon juice in a small skillet and cook over medium-high heat until reduced by two-thirds, about 15 minutes. You should have about 2 tablespoons left. Remove from the heat and reserve until ready to use.
In a medium bowl whisk together the shallots and mustard. Slowly drizzle in the reduced citrus juice and the champagne vinegar. Add the oil in a thin, steady stream, whisking constantly. Season lightly with salt and freshly cracked pepper.
In a mixing bowl, combine the hearts of palm, orange segments, baby spinach, and red onion. Season with salt and freshly cracked black pepper, and toss to combine. Divide between 2 chilled salad plates, and drizzle evenly with the prepared vinaigrette. Serve with extra ground black pepper if desired.
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