Soak the skewers: If using wooden skewers, soak them in water for at least 20 minutes.
Make the marinade: Place olive oil, lemon zest, lemon juice, honey, garlic, paprika, red pepper flakes, parsley salt, and pepper in a bowl. Give it a whisk until fully combined. Add the shrimp into the bowl and toss to coat. Cover it with plastic wrap and refrigerate for 30 minutes.
If using a gas grill: Turn half of the burners to high and let them preheat for 10 minutes or until it reaches 400 F degrees.
If using a charcoal grill: If using a charcoal grill, fill up your charcoal chimney and light a fire starter underneath it. Once the charcoal is ashed over completely, dump it into the grill and place the cooking grate on your grill. Let it heat up to 400 degrees.
If using a grill pan on cooking on the stovetop: Heat grill pan over medium heat until hot.
Skewer the shrimp: Meanwhile, thread shrimp on skewers starting from the thickest part of the shrimp and arranging 5-6 shrimp per skewer. Place on a plate and set aside.
Grill: If you are using a gas or charcoal grill, grill shrimp skewers on direct heat for 2-3 minutes or as soon as it turns pink along the edges and then flip over and cook for another 2 minutes or until it is lightly charred. If grilling on a grill pan, cook shrimp for 3 to 3 ½ minutes on each side.
Serve with lemon wedges on the side.