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Step 1
Heat the oven to 450°F with the rack in the middle position. While the oven is heating up, pat the chicken dry with paper towels. Sprinkle kosher salt liberally (about 2 teaspoons) on both sides of the chicken pieces.
Step 2
Heat a 12-inch oven-safe heavy bottomed skillet over medium high heat. When the pan is hot, swirl in the ghee.
Step 3
Add the chicken pieces skin-side down in the hot pan. Sear, undisturbed, until nicely browned and crispy, about 4 to 6 minutes. While the skin is crisping, add some freshly ground black pepper to the meaty side.
Step 4
When the skin is golden brown, flip the pieces over and cook for 2 minutes more. Then, transfer the chicken to a platter. (Note: The chicken is not ready to eat at this point. You need to finish cooking it in the oven.)
Step 5
Turn the heat off and add the shallots to the empty pan. It’s plenty hot and you don’t want to burn the shallots. Cook, stirring occasionally, until slightly softened, about 1 minute.
Step 6
Turn the heat to medium and toss in the summer squash and a sprinkle of salt. Saute, stirring occasionally, until the squash is lightly browned and tender, about 3 to 5 minutes.
Step 7
Stir in the cherry tomatoes and garlic cloves. Cook until garlic is fragrant and some of the tomatoes have burst, about 1 minute.
Step 8
Pour in the broth and balsamic vinegar and stir well to combine. Add the thyme sprigs.
Step 9
Bring to a simmer and taste and adjust sauce for seasoning with more salt if needed.
Step 10
Tuck in the chicken pieces, skin-side up, making sure the skin stays above the broth.
Step 11
Transfer the pan to the hot oven and roast the chicken for 15-20 minutes. The dish is ready when the internal temperature of the chicken reaches at least 165°F (aim for 150°F to 155°F for chicken breast) and the vegetables have softened into a chunky sauce.
Step 12
Remove the skillet from the oven. Discard the thyme sprigs and garnish with fresh basil. Serve immediately!