In a medium-sized bowl, whisk together lemons, garlic, 3 tbsp olive oil, salt, and pepper. Add raw chicken tenders and stir to coat well. Cover with plastic wrap and let marinate while you prepare your carrots, or marinate up to two hours in the refrigerator if preparing ahead of time.
To prepare the roasted rainbow carrots, preheat your air fryer to 400 degrees. In a medium-sized bowl, combine all ingredients listed for roasted carrots and toss to combine.
Once the air fryer has preheated, set timer to 12 minutes, add seasoned carrots, and roast at 400 degrees, shaking carrots halfway through.
Meanwhile, place panko bread crumbs and flour in a small dish and toss gently to combine. Remove chicken from marinade bowl and set aside the bowl with your marinade left inside; you'll use this later as part of the sauce. Coat both sides of chicken gently in the panko/flour mixture.
Then, heat a deep sauté pan with 1/4 cup olive oil and 2 tbsp butter over medium high heat. Brown the chicken, one layer at a time, until each side is golden brown; approximately three minutes per side. If your oil becomes too hot, lower your heat to medium-medium low. Some of your oil may burn off during the cooking process. This is okay; just add a little more olive oil to re-coat the bottom of the pan.
Remove chicken from heat and place on paper towels to soak the excess oil. Then, keeping the olive oil and browned bits in your sauté pan, lower the heat to medium low and add in the leftover marinade. If your pan is too hot, lower the heat to low.
Add in white wine, capers, and remaining 2 tbsp butter to your sauté pan. Stir to combine, thickening and reducing down to 1/3 the original amount, approximately 5-10 minutes. Season with kosher salt to your taste preference.
Once your sauce has reduced and heated through, drizzle over chicken and top with parsley and parmesan cheese to serve.