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Step 1
Position a rack in the middle of the oven and preheat to 425 degrees.
Step 2
In a large bowl, mix together 3 tablespoons of the olive oil, the garlic, lemon zest, oregano, salt and paprika or black pepper. Add the chicken or cauliflower and, using your hands, rub the mixture into the meat or vegetable.
Step 3
On a large, rimmed baking sheet, combine the potatoes and artichoke hearts. Drizzle with the remaining olive oil, and toss.
Step 4
Lay the quarters atop the potatoes and artichoke hearts and roast for 30 minutes. Toss the potatoes and artichoke hearts so they brown evenly. Rotate the pan, then roast for an additional 20 to 30 minutes, or until the chicken is cooked — an instant-read thermometer should read 165 degrees when inserted into the thickest part of the thigh — or cauliflower is crisp on the outside but fork-tender all the way through.
Step 5
Remove the pan from the oven and add the olives, olive brine and lemon juice. Use a spatula or wooden spoon to help mix any browned bits into the sauce, top with chopped fresh parsley, if using, and serve family style.