Season the chicken cutlets generously with kosher salt and black pepper on both sides. In a shallow dish, combine all-purpose flour and grated Parmesan. Dredge each cutlet in the flour mixture until thoroughly coated. Set aside.

Heat a large skillet over medium-high heat and add extra virgin olive oil. Carefully place the chicken cutlets into the skillet and sear for about 3-5 minutes per side until golden brown. Remove the cutlets and keep warm.

In the same skillet, reduce heat to medium and add salted butter along with the asparagus. Sprinkle with salt and pepper, and sauté for about 5 minutes until tender. Transfer asparagus to the plate with chicken.

Add minced garlic and capers to the skillet, sautéing for about 1 minute. Pour in dry white wine and fresh lemon juice, scraping browned bits. Bring to a simmer and let it reduce for 2-3 minutes. Return the chicken, spoon sauce over, and simmer for an additional 5 minutes.

In a pot, bring water to a boil and gradually whisk in instant polenta. Continue whisking as it thickens for 3-5 minutes as per instructions. Stir in butter, grated Parmesan, and basil pesto until combined.

To serve, spoon polenta onto plates, top with chicken, and arrange sautéed asparagus. Drizzle with the sauce and garnish with herbs or lemon zest if desired.