Prepare your shrimp. If tails are on, you may leave them for look and grip; otherwise remove tails. Pat shrimp dry with paper towel so they’ll absorb marinade and sear nicely.
Make the marinade. In a medium bowl whisk together the olive oil, lemon juice, lemon zest, chopped basil, chopped parsley, tarragon, smoked paprika, salt and pepper.
Marinate the shrimp. Add the shrimp to the bowl, toss gently until fully coated. Cover and refrigerate for 10-15 minutes (no more than 20 minutes, as citrus starts to “cook” the shrimp).
Skewer the shrimp. Thread about 5–6 shrimp per skewer, spacing slightly so heat circulates and they cook evenly.
Preheat the grill. Heat your grill or grill pan to medium-high (around 375-400°F / 190-200°C). Oil the grates or lightly brush oil.
Grill the kabobs. Place shrimp skewers on the grill. Cook for ~3 minutes on the first side until the underside is pink and opaque about ⅔ way up the shrimp. Flip gently and grill another ~2-3 minutes until fully opaque, the shrimp slightly curled, edges showing a light char. Remove promptly to prevent over-cooking.
Drizzle & serve. If using the finishing drizzle, whisk the olive oil, lemon juice and smoked paprika and drizzle over the hot skewers. Scatter the torn basil leaves on top and serve immediately while shrimp still glisten and steam rises.