Heat the oven to 425°F.
On 1 sheet pan, toss the potatoes with 1 tablespoon [2 TBL] oil and season generously with salt and pepper. Spread in an even layer and roast until just tender, 15 to 20 minutes (they will finish roasting in Step 3).
While the potatoes roast, prepare the chicken.

• Pat the chicken dry with a paper towel; cut each breast in half horizontally to form 2 cutlets, for a total of 4 [8] cutlets. Season the cutlets generously with salt and pepper.
• Set aside 1 tablespoon [2 TBL] flour for the piccata sauce. On a plate or shallow bowl, season the remaining flour generously with salt and pepper and spread in an even layer.

Working with 1 cutlet at a time, dredge the chicken in the flour, turning to coat; shake off any excess. In a large frying pan over medium heat, warm 1 tablespoon [2 TBL] oil until hot but not smoking. Add the chicken and cook, turning once, until lightly browned and cooked through, 3 to 4 minutes per side. Transfer to a plate. Do not clean the pan.
While the chicken cooks, prepare the zucchini and finish the potatoes.

• Cut the zucchini in half lengthwise; cut each half lengthwise into thirds, then crosswise into 2-inch lengths.
• In a small bowl, stir together the Parmesan, garlic-herb blend, and as many chile flakes as you like.

On the second sheet pan, arrange the zucchini in a single layer, brush with 1 tablespoon [2 TBL] oil, and season with salt and pepper. Sprinkle with as much Parmesan-herb blend as you like; set aside any remaining blend for serving.
Remove the potatoes from the oven. Using the bottom of a cup, gently smash the potatoes until the skins break and toss with 1 tablespoon [2 TBL] oil. Roast until the potatoes and zucchini are tender, 10 to 15 minutes.
While the vegetables roast, prepare the piccata sauce.

• Rinse the capers, then coarsely chop them.
• Zest and juice the lemon, keeping the zest and juice separate. [Zest both lemons; juice 1 lemon. Save the remaining zested lemon.]
• Strip the parsley leaves from the stems; coarsely chop the leaves. Set aside half for garnish.

In the same pan used for the chicken, add 1 tablespoon [2 TBL] butter (from your pantry) or oil and heat over medium heat until hot but not smoking. Stir in the remaining 1 tablespoon [2 TBL] flour and using a fork or whisk, stir until the flour is incorporated and starting to brown, 2 to 3 minutes. While whisking, stir in the capers, lemon juice, and ½ cup [1 cup] water. Bring to a boil, reduce to a simmer, and cook, scraping up any browned bits from the bottom of the pan, until thickened slightly, 3 to 4 minutes.
Remove from the heat, stir in the lemon zest and half the parsley, and season to taste with salt and pepper. Add the chicken and cook over medium heat until warmed through, 1 to 2 minutes.

Transfer the chicken to individual plates and top with the piccata sauce. Arrange the potatoes and zucchini alongside. Sprinkle with any remaining Parmesan-herb blend, garnish with the remaining parsley, and serve.