In a large bowl whisk the marinade ingredients; add the artichoke hearts, tomatoes, eggplants, and onion. Let marinate at room temperature for 15 minutes.
Prepare the grill for direct cooking over medium heat (350° to 450°F).
Remove the vegetables from the bowl and shake off any excess marinade. Brush the cooking grates clean. Grill the vegetables over direct medium heat, with the lid closed as much as possible, for about 6 minutes, turning once. Remove from the grill and roughly chop. Put the vegetables into a medium saucepan and add the chicken broth. Simmer over medium heat for 15 minutes. Remove from the heat and keep warm.
In a small bowl mix the bread crumbs, salt, and pepper. Roll each chop in the bread crumb mixture. Allow the chops to stand at room temperature for 15 to 30 minutes before grilling.
In a medium saucepan combine the chicken broth and butter; bring to a boil. Add the polenta and stir well. Reduce the heat and simmer for 12 minutes, covered. Remove from the heat and stir in the sour cream.
Grill the chops over direct medium heat, with the lid closed as much as possible, until cooked to your desired doneness, 9 to 11 minutes for medium rare, turning once or twice. Serve warm with the grilled vegetables and creamy polenta.
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