Prepare a grill for medium heat.
Whisk together the shallots, Dijon, honey and balsamic in a medium bowl. Slowly add 3 tablespoons olive oil while whisking to emulsify. Whisk in 1/4 teaspoon salt and a few grinds of pepper.
Brush the radicchio on both sides with olive oil and season lightly with salt and pepper. Grill until charred in spots and slightly wilted, turning once, about 8 minutes.
Meanwhile, toss the shrimp with a splash of olive oil, and sprinkle with 1/4 teaspoon salt and some pepper. Grill, turning once, until just cooked through, about 3 minutes per side.
Divide the radicchio and shrimp among small plates, drizzle with vinaigrette and sprinkle with parsley leaves. Serve warm or at room temperature.
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