Chicken Primavera

Name: Chicken Primavera
Ingredients: ½ cup all-purpose flour; 1½ tsp. Diamond Crystal or 1 tsp. Morton kosher salt, plus more; ½ tsp. freshly ground black pepper, plus more; 2 large skinless, boneless chicken breasts (about 1½ lb. total), patted dry; ¼ cup plus 1 Tbsp. grapeseed or vegetable oil; 5 oz. frozen pearl onions or 1½ cups coarsely chopped scallions (pale green and white parts only); 5 garlic cloves, thinly sliced; ½ cup heavy cream; ½ cup low-sodium chicken broth (Better Than Bouillon also works great here); ⅓ cup fresh lemon juice; 8 oz. asparagus, woody ends trimmed, thinly sliced on a diagonal; 1¼ cups shelled fresh peas (from about 1¼ lb. pods) or frozen peas; 1 tsp. Dijon mustard; ½ cup very coarsely chopped dill, divided; Shaved Parmesan (for serving; optional)