Season Chicken: Place the chicken breasts on a work surface and season both sides evenly with kosher salt, black pepper, and smoked paprika.
Preheat Grill: Heat a grill or grill pan over medium-high heat until hot.
Grill Chicken First Side: Place the chicken on the grill and cook for about 5–6 minutes until grill marks form and the chicken releases easily.
Flip Chicken: Turn the chicken and cook another 5–6 minutes until nearly cooked through.
Make Peach Glaze: In a mixing bowl, combine peach preserves, green onions, 1 tablespoon olive oil, minced garlic, sriracha sauce, 1 tablespoon Dijon mustard, and 2 tablespoons soy sauce. Whisk until smooth.
Glaze and Finish Chicken: Brush the glaze generously over the chicken. Flip and brush again, cooking for another 2–3 minutes until the sauce caramelizes and the chicken is fully cooked. Remove from heat and rest.
Prep Asparagus: Trim the woody ends of the asparagus. Thread onto skewers to keep them together for easy grilling.
Season Asparagus: Brush the asparagus with 1 tablespoon olive oil.
Grill Asparagus: Place on the grill and cook for 4–6 minutes, turning occasionally, until tender and lightly charred.
Make Asparagus Dressing: In a small bowl, whisk together remaining 1 tablespoon Dijon mustard, 1 tablespoon soy sauce, 1 tablespoon olive oil, and a small amount of minced garlic (if available from earlier prep).
Dress Asparagus: Transfer asparagus to a serving dish and drizzle with the dressing. Toss lightly to coat.
Serve: Slice the chicken if desired and serve alongside the chargrilled asparagus. Spoon extra glaze over the chicken for maximum flavor.