Step 1

Whisk together ½ cup all-purpose flour, 1½ tsp. Diamond Crystal or 1 tsp. Morton kosher salt, and ½ tsp. freshly ground black pepper in a medium bowl; set aside.

Step 2

Slice 2 large skinless, boneless chicken breasts (about 1½ lb. total), patted dry, on a cutting board in half lengthwise to create 4 cutlets. Working one at a time, gently pound each cutlet between 2 sheets of plastic wrap to about ½" thick. Transfer cutlets to reserved bowl of seasoned flour and toss to coat very well. Working one at a time, shake off excess flour and transfer cutlets to a plate.

Step 3

Heat ¼ cup grapeseed or vegetable oil in a large skillet over medium-high. Add 2 cutlets to pan and cook, undisturbed, until golden brown underneath, about 3 minutes. Turn cutlets over and cook until golden brown on other sides, about 3 minutes. Transfer to a platter or plates and repeat with remaining 2 cutlets.

Step 4

Remove pan from heat and carefully wipe out with a paper towel to remove most of the excess oil and browned bits. Add remaining 1 Tbsp. grapeseed or vegetable oil to pan and heat over medium. Add 5 oz. frozen pearl onions or 1½ cups coarsely chopped scallions (pale green and white parts only) and 5 garlic cloves, thinly sliced, and cook, stirring occasionally, until onions begin to turn translucent, about 4 minutes if using pearl onions or 2 minutes if using scallions. Add ½ cup heavy cream, ½ cup low-sodium chicken broth, and ⅓ cup fresh lemon juice. Bring to a simmer and cook until reduced by a third, about 3 minutes.

Step 5

Add 8 oz. asparagus, woody ends trimmed, thinly sliced on a diagonal, and 1¼ cups shelled fresh peas (from about 1¼ lb. pods) or frozen peas and cook, stirring, until asparagus is crisp-tender, about 2 minutes. Mix in 1 tsp. Dijon mustard followed by ¼ cup very coarsely chopped dill; season with salt.

Step 6

Spoon vegetables and sauce over cutlets. Season with more pepper and top with shaved Parmesan (if using) and remaining ¼ cup very coarsely chopped dill.