Step 1
Holding a long knife parallel to cutting board and working one at a time, slice 2 large skinless, boneless chicken breasts (about 1½ lb. total), patted dry, in half, starting on a long side, to create 4 cutlets. Working one at a time, lightly pound cutlets between 2 sheets of plastic wrap with a meat mallet or small heavy skillet to an even ¼” thick. Season on both sides with kosher salt and freshly ground pepper.
Step 2
Meanwhile, cook 8 oz. penne in a large pot of boiling salted water, stirring occasionally, until very al dente, about 1 minute less than package directions. Drain pasta, reserving 2 cups pasta cooking liquid.
Step 3
Mix ½ cup (63 g) all-purpose flour and 2 oz. Parmesan, finely grated (about 1 cup), on a plate with your hands. Whisk 1 large egg in a shallow bowl just to blend. Working with 1 cutlet at a time, dredge in flour mixture, shaking off excess, then dip in egg, letting excess drip back into bowl. Dredge in flour mixture again, pressing to adhere in a coarse layer.
Step 4
Heat ¼ cup extra-virgin olive oil in a large high-sided skillet over medium. Working in 2 batches and adding more oil between batches if needed, cook cutlets, turning halfway through, until deep golden brown, 6–8 minutes. Transfer to a cutting board.
Step 5
Cook 1 lb. asparagus, trimmed, cut into 1″ pieces, and 8 oz. green beans, trimmed, cut into 1″ pieces, in same skillet, stirring often, until tender, about 4 minutes. Add 6 garlic cloves, finely chopped; cook, stirring constantly, until fragrant, about 1 minute. Add 1 cup frozen peas, ¾ cup heavy cream, 4 Tbsp. unsalted butter, cut into pieces, 1 Tbsp. white miso, pasta, and remaining 2 oz. Parmesan, finely grated (about 1 cup). Cook, stirring and adding pasta cooking liquid as needed, until a thick, glossy sauce forms. Remove from heat and stir in zest and juice of 1 large lemon; season with salt and pepper.
Step 6
Slice chicken and arrange on top of pasta; scatter thin strips of lemon zest over.
