Heat a charcoal or gas grill to high for direct grilling. Brush the cut sides of the oranges and radicchio with some olive oil and season with salt and pepper. Put the oranges and radicchio cut-side down on the grill and cook just until charred and slightly softened. Transfer the radicchio to a platter.
Squeeze the orange juice into a bowl and whisk in the almonds, vinegar, parsley, honey, mustard and salt and pepper to taste. Slowly whisk in the olive oil until emulsified. Let sit at room temperature for at least 15 minutes before serving.
Brush the trout fillets with canola oil and sprinkle with salt and pepper on both sides. Grill until golden brown and slightly charred on both sides and just cooked through, about 3 minutes per side. Remove to the platter with the radicchio and immediately drizzle with the vinaigrette. Garnish with parsley leaves.