In a medium bowl, whisk together the lemon zest, lemon juice, minced garlic, olive oil, Dijon mustard, chopped parsley, salt, and pepper until fully combined and emulsified.

Add the salmon cubes to the marinade and gently toss to coat every piece. Let marinate at room temperature for 15 to 30 minutes. Do not exceed 30 minutes as the lemon juice will begin to break down the fish texture.

If using wooden skewers, soak them in water for at least 30 minutes before use to prevent burning. Thread the marinated salmon cubes onto the skewers, leaving a small gap between pieces for even cooking. Lightly pat off any excess marinade before grilling.

Preheat your grill or grill pan to medium-high heat (around 400°F). Lightly oil the grill grates. Place the skewers on the grill and cook undisturbed for 2 to 3 minutes per side, until the salmon is opaque, lightly charred, and cooked through. The internal temperature should reach 125°F to 130°F for medium or 145°F for fully cooked.

Remove the skewers from the grill and let them rest for 2 minutes. Transfer to a serving platter, garnish with additional fresh parsley and lemon slices, and serve immediately.