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Step 1
Heat olive oil in a large dutch oven or wide, heavy-bottomed pot or pan with high sides over medium-high heat.
Step 2
Season chicken thighs all over with salt and pepper, then place 4 of them in the pan skin-side-down and cook until browned, about 5 minutes. Flip and cook until browned on the other side, about 5 minutes more, then transfer to a plate and repeat with the remaining chicken thighs.
Step 3
Lower the heat, then add the anchovies to the pan and stir until they start to break down and dissolve in the fat. Add the garlic and rosemary and sauté for about a minute.
Step 4
Deglaze the pan with vinegar, white wine and water, then nestle the chicken pieces back into the pan. Bring the sauce up to a boil, then reduce the heat to keep it at a low simmer. Spoon some of the sauce over each chicken thigh, then cover and cook for about 20 minutes, or until the chicken is fully cooked and tender.
Step 5
Remove the lid and allow the sauce to reduce and thicken for about 10 minutes more.
Step 6
Remove the rosemary sprigs and garlic cloves if desired, then serve.