Preheat a smoker to 250°F. Lightly oil the smoker grates with the olive oil to help prevent sticking.

In a large bowl, combine the ground turkey, panko, egg, drained green chiles, jalapeño, onion, garlic, smoked paprika, salt, and black pepper. Mix gently until combined, taking care not to pack the meat mixture tightly.

Place half of the turkey mixture on a sheet of parchment and shape it into a rectangle. Arrange the pepper jack strips lengthwise down the center, leaving a border around the edges. Cover with the remaining turkey mixture and pinch the seams closed so the cheese is fully enclosed. Shape into a compact loaf.

Transfer the loaf to the prepared smoker grates. Smoke until the center reaches 160°F, checking with an instant-read thermometer inserted into the meat without touching the cheese.

Brush the top and sides with half of the barbecue sauce during the last 20 minutes of smoking. Remove the loaf when it reaches temperature, then brush with the remaining sauce.

Rest the meatloaf for 10 minutes before slicing. Cut gently so the melted pepper jack stays inside each slice.