1. Begin by patting the chicken breasts or thighs dry with a paper towel to ensure a crispy crust when grilling.
2. Mix olive oil, garlic powder, paprika (optional), salt, and black pepper in a small bowl, and brush this mixture over both sides of the chicken.
3. Drizzle the lemon juice over the chicken and let it sit for 15-30 minutes to marinate and infuse flavor.
4. Preheat your grill or grill pan over medium-high heat for even cooking.
5. Place the chicken on the grill, cooking for 5-7 minutes per side until grill marks are visible and the internal temperature reaches 165°F (73.9°C).
6. Remove the cooked chicken from the grill, tent it with foil, and let it rest for 5-10 minutes to lock in the juices.
7. In a medium skillet, melt the unsalted butter over medium heat and sauté the minced onion and garlic until fragrant and softened (about 2-3 minutes).
8. Pour in the chicken broth and let it cook for another 3-5 minutes to reduce slightly.
9. Reduce heat to low and stir in the heavy cream, allowing the sauce to simmer for 5 minutes, stirring occasionally, until slightly thickened.
10. If using cornstarch, mix it with a tablespoon of water and whisk into the sauce to achieve the desired consistency.
11. Add the fresh dill and lemon juice to the sauce, and season with salt and pepper to taste, adjusting if needed.
12. Remove the sauce from heat once thickened and flavorful to prevent splitting.
13. Place the grilled chicken on a serving plate and spoon the creamy dill sauce generously over each piece.
14. Garnish with additional fresh dill for a polished presentation and serve immediately.
15. Pair with your choice of sides, such as roasted vegetables, a crisp green salad, or fluffy rice, for a complete meal.