Trim the asparagus spears by snapping off the woody ends, then set aside. Juice half the lemon and zest the other half, keeping them separate. Pat the chicken breasts dry with paper towels—this helps them brown better on the grill. In a small bowl, combine the kosher salt, cracked black pepper, and smoked paprika to create your seasoning blend. Have the provolone cheese slices, fresh basil leaves, and all other ingredients measured and ready before you start assembling.
Place each chicken breast on a cutting board. Using a sharp knife, carefully slice horizontally through the thickest part of each breast, stopping about ½ inch from the edges to create a pocket—don't cut all the way through. Gently open each breast like a book. Lay a slice of provolone cheese on one side, top with 2 fresh basil leaves, then arrange 3 asparagus spears on top. Fold the chicken back over the filling and secure with 2-3 toothpicks along the seam to keep everything together during grilling.
Brush both sides of each stuffed chicken breast with extra virgin olive oil. Sprinkle the seasoning blend from Step 1 evenly over all sides. Drizzle the lemon juice over the chicken and sprinkle the lemon zest as well—I like to do this right before grilling so the zest stays bright and doesn't dry out on the raw chicken. Let the seasoned chicken sit for about 2 minutes while you heat the grill.
Heat your grill to medium-high (around 375-400°F). Once hot, carefully place the stuffed chicken breasts on the grill grates. Close the lid and grill for 6-7 minutes on the first side until you get nice grill marks. Flip the chicken and grill for another 6-7 minutes with the lid closed. Turn once more to ensure even cooking, grilling for another 2-3 minutes. The chicken is done when it reaches an internal temperature of 165°F at the thickest part.
Remove the grilled chicken from the heat and let it rest on a warm plate for 5 minutes—this allows the juices to redistribute throughout the meat, keeping it tender and moist. While the chicken rests, combine the sour cream, garlic powder, Dijon mustard, and dry white wine in a small saucepan over medium-low heat. Stir gently until the sauce is warm and smooth, about 2-3 minutes. Don't let it boil or the sour cream may curdle.
Carefully remove the toothpicks from the rested chicken breasts. Place each chicken breast on a serving plate and drizzle generously with the warm sour cream sauce. Serve immediately while the chicken is still hot and the sauce is warm.