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In a large bowl, whisk together ¼ cup olive oil, vinegar, and mustard. Add chicken thighs and toss to coat. Cover and refrigerate for 30 minutes or up to 4 hours. Preheat oven 425°. In a large skillet over medium-high heat, heat remaining 2 tablespoons oil. Shake off excess marinade from chicken and season all over with salt and pepper. Add, skin side-down, and cook until seared and golden, about 6 minutes. Flip chicken and cook until seared on other side, about 6 minutes. Scatter tomatoes and zucchini around chicken. Season vegetables with salt and pepper, then transfer skillet to oven and bake until chicken is cooked through, about 15 minutes more. Garnish with Parmesan and basil before serving.