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In a blender, purée the herbs, oil, Parmesan, garlic and lemon. Season the sauce with salt and pepper.
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In a baking dish, drizzle the meat with half the sauce. Let marinate for 15 minutes or overnight. Refrigerate the remaining sauce until ready to serve.
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Drain the meat and discard the marinade. In a lightly oiled ridged skillet over medium-high heat, grill the meat for about 4 minutes on each side or until the desired doneness. Set aside on a plate. Cover and let rest for 5 minutes.
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Serve the chops with the cooked beet cubes and the avocado slices. Drizzle with the reserved sauce.
NOTE
The meat and marinade can be frozen in a vacuum-packed bag or a sealable plastic bag the day before. As a bonus, when frozen in a marinade, meat is less altered by thawing.