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Step 1
Heat the oven to 400°F with a rack in the middle position. Cut a 10-inch piece of foil and set the garlic head cut side up on top. Drizzle the garlic with oil and sprinkle with salt and pepper. Enclose the head in the foil and place in the oven. Roast for about 30 minutes.
Step 2
Meanwhile, in a 12-inch nonstick oven-safe skillet, combine the chorizo and 1 tablespoon oil; cook over medium-high, stirring, until the chorizo is sizzling and renders some of its oil, about 3 minutes. Using a slotted spoon, transfer to a medium bowl; set aside.
Step 3
To the fat remaining in the skillet, add 1 tablespoon of the remaining oil, then add the potatoes in an even layer. Cook over medium-high, stirring occasionally, until lightly browned, 4 to 5 minutes. Using the slotted spoon, transfer the potatoes to the bowl with the chorizo.
Step 4
To the skillet still over medium, add the remaining 1 tablespoon oil along with the onion, the minced garlic and a pinch of salt. Cook, stirring occasionally, until the onion is softened, 2 to 3 minutes. Add the smoked paprika and cook, stirring, until fragrant, about 30 seconds. Add the rice, chopped tomatoes, chickpeas and the potato-chorizo mixture. Stir in the broth and ½ teaspoon each salt and pepper, then bring to a boil over medium-high. Reduce to medium and simmer, uncovered and stirring occasionally, until some of the rice grains remain on the surface instead of sinking to the bottom, about 5 minutes.
Step 5
Unwrap the garlic and nestle it cut side up in the center of the skillet. Arrange the tomato slices around the garlic; lightly press them in so they are just covered with liquid but not fully submerged in the rice mixture. Carefully transfer the skillet to the oven and bake until the liquid is absorbed and the potatoes are tender, 10 to 12 minutes.
Step 6
Remove from the oven (the handle will be hot), cover with a kitchen towel and a lid, then let rest for about 10 minutes. Sprinkle with the parsley. Serve directly from the skillet.